Davor Dragicevic, Yeor Hafouta
We prove a quenched almost sure invariance principle for certain classes of random distance expanding dynamical systems which do not necessarily exhibit uniform decay of correlations.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
继续探索
Let $T \colon M \to M$ be a nonuniformly expanding dynamical system, such as logistic or intermittent map. Let $v \colon M \to \mathbb{R}^d$ be an observable and $v_n = \sum_{k=0}^{n-1} v \circ T^k$ denote the Birkhoff sums. Given a probability measure $μ$ on $M$, we consider $v_n$ as a discrete time random process on the probability space $(M, μ)$. In smooth ergodic theory there are various natural choices of $μ$, such as the Lebesgue measure, or the absolutely continuous $T$-invariant measure. They give rise to different random processes. We investigate relation between such processes. We sh…
Almost Sure Invariance Principle For Nonuniformly Hyperbolic Systems
我们证明了一个几乎必然的不变原理，是有效的一般类的非一致膨胀和非一致双曲动力系统。离散时间系统和流的覆盖这一结果。特别地，该结果适用于有限视界平面周期洛仑兹流。统计极限定律，如中心极限定理、重对数定律及其函数形式，都是直接的结果。
We prove the almost sure invariance principle with rate $o(n^{\varepsilon})$ for every $\varepsilon > 0$ for Hölder continuous observables on nonuniformly expanding and nonuniformly hyperbolic transformations with exponential tails. Examples include Gibbs-Markov maps with big images, Axiom A diffeomorphisms, dispersing billiards and a class of logistic and Hénon maps. The best previously proved rate is $O(n^{1/4} (\log n)^{1/2} (\log \log n)^{1/4})$. As a part of our method, we show that nonuniformly expanding transformations are factors of Markov shifts with simple structure and natural metri…
Mixing properties of a class of nonuniformly expanding maps. Application to H{ö}lderian invariance principles
本文研究返回时间仅具有p>1阶弱矩的非一致扩张映射的混合性质，并由此建立Hölder连续观测量部分和过程的Hölder不变原理，进而将结果推广到间歇映射及BV观测量。
Stochastic-like behaviour in nonuniformly expanding maps
这是一个显着的扩展版本的调查文件“混合和衰减的相关性在非均匀扩展的地图：一个调查的最新结果”数学/0301319。我们讨论了最近的结果衰减的相关性的非一致膨胀的地图。在整个讨论中，我们解决的问题，为什么不同的动力系统有不同的衰减率的相关性，以及如何这可能反映潜在的几何特征的系统。我们还给出了一些结果的详细草图，如马氏扩张映射的绝对连续不变测度的存在性，某些一维映射中诱导马氏扩张映射的构造，以及证明了这样的构造对于二次族中的正概率映射集是可以进行的。
Absolutely Continuous Invariant Measures for Nonuniformly Expanding Maps
对于$\Bbb R^m$中的一类非一致扩张映射，构造了一个绝对连续的不变测度.我们扩展到我们的情况下，以前用于扩大映射的准Hölder空间的技术。我们给出了一般条件，并提供了应用我们的结果的例子。
Decay of correlations for nonuniformly expanding systems
我们估计一般非均匀膨胀动力系统的相关性衰减的速度，使用的时间估计系统需要真正扩大。我们的方法可以处理快速衰减，如指数或拉伸指数。特别证明了Alves-Viana映射的相关性在$O(e^{-c \sqrt{n}})$中衰减。
On $\mathrm{C}^1$-class local diffeomorphisms whose periodic points are nonuniformly expanding
本文利用筛选-跟踪组合证明了闭流形$M^n$的任意$\mathrm{C}^1$类局部自同构$f$在其周期点集$\mathrm{Per}(f)$的闭包$\mathrm{Cl}_{M^n}(\mathrm{Per}(f))$上一致扩张，如果它在$\mathrm{Per}(f)$上非一致扩张.
Decay of correlations for nonuniformly expanding systems with general return times
我们利用良好的诱导方案给出了非均匀膨胀系统相关性衰减的统一处理。除了比以前的治疗更基本，我们的结果持有一般可积的返回时间函数在相当温和的条件下的诱导计划。
Nonuniformly expanding 1d maps with logarithmic singularities
对于圆上具有临界点和对数奇点且导数爆破到无穷大的一类参数化映射族，构造了对应于非一致扩张映射的参数的正测度集.这意味着周期扰动微分方程中耗散同宿纠缠的“混沌”动力学的存在。
Rates in almost sure invariance principle for nonuniformly hyperbolic maps
本文在不假设稳定叶指数压缩的条件下，为非一致双曲映射证明了误差速率接近最优的几乎必然不变原理，并利用双侧更新 Markov 转移的半共轭方法，首次覆盖了 Bunimovich flowers 等缓慢混合系统。
Every expanding measure has the nonuniform specification property
研究了具有正李雅普诺夫指数的保遍历概率的自同态的双曲时间的丰富性和非空性，得到了几乎每个动力球都存在周期关于球长次线性增长的周期点.特别地，我们得出结论，任何遍历测度与积极的李雅普诺夫指数满足非一致规格性质。作为推论，我们（重新）得到了球的常返性的李雅普诺夫指数估计，并证明了任何扩张测度都是周期点上Dirac测度的极限.
The almost sure invariance principle for unbounded functions of expanding maps
考虑了$[0,1]$的两类分段扩张映射$T$：一类Perron-Frobenius算子在有界变差函数空间中具有谱间隙的一致扩张映射和一类中性不动点在零的扩张映射.在这两种情况下，我们给出了一大类无界函数$f$，其中$f\circ T^i$的部分和满足几乎必然不变原理。这个类包含分段单调函数（具有有限数量的分支），使得：-对于均匀扩展的映射，它们相对于绝对连续不变的概率测度是平方可积〔的〕的。- 对于具有位于零的中性不动点的映射，它们满足关于绝对连续不变概率测度的（最佳）尾部条件。
For a large class of quickly mixing dynamical systems, we prove that the error in the almost sure approximation with a Brownian motion is of order O((log n)^a) with a $\ge$ 2. Specifically, we consider nonuniformly expanding maps with exponential and stretched exponential decay of correlations, with one-dimensional H{ö}lder continuous observables.
Almost Sure Central Limit Theorems and the Erdos-Renyi law for Expanding Maps of the Interval
对区间上的一大类扩张映射，证明了Lipschitz观测量的部分和满足几乎必然的中心极限定理（ASCLT）.事实上，我们在Kantorovich度量中提供了收敛速度。部分和的最大值也服从ASCLT。关键工具是最近得到的一个指数不等式。然后，我们得到了Lipschitz观测量的移动平均的上确界的几乎必然收敛速度（Erdos-Renyi型定律）。最后，我们应用熵估计ASCLT的，refi ne Shannon-McMillan-Breiman和Ornstein-Weiss定理。
In the present paper, we study the distribution of the return points in the fibers for a RDS (random dynamical systems) nonuniformly expanding preserving an ergodic probability, we also show the abundance of nonlacunarity of hyperbolic times that are obtained along the orbits through the fibers. We conclude that any ergodic measure with positive Lyapunov exponents satisfies the nonuniform specification property between fibers. As consequences, we prove that any expanding measure is the limit of probability measure whose measures of disintegration on the fibers are supported by a finite number …
Statistical properties of nonuniformly expanding 1d maps with logarithmic singularities
对于圆上的某个参数化映射族，具有临界点和对数奇点，其中导数爆破到无穷大，在[19]中构造了一个参数的正测度集，对应于表现非一致双曲行为的映射。对于这些参数，我们证明了存在绝对连续的不变测度具有良好的统计性质，如指数衰减的相关性。结合我们的构造和奇点的对数性质，我们得到了一个正方差的中心极限定理，对任何非常数Hölder连续观测。
Nonuniform expansion and diffusive noise imply random horseshoes and random Young towers
本文提出随机马蹄概念，证明非均匀扩张随机动力系统在扩散噪声下随机马蹄稠密且存在退火指数尾部的随机Young塔。
Schmidt's Game and Nonuniformly Expanding Interval Maps
研究Manneville-Pomeau映射，证明前向轨道避开左端点为0的区间的点集在Schmidt博弈中强获胜，该集具有稠密性、满Hausdorff维数和可数交性质。
Rigorous pointwise approximations for invariant densities of nonuniformly expanding maps
我们使用一个Ulam型离散化方案，提供逐点逼近的不变密度的区间映射的中性不动点。我们证明了近似不变密度以$C^*\cdot\frac{\ln m}{m}$的速率逐点收敛到真密度，其中$C^*$是可计算的固定常数，$m^{-1}$是离散化的网格步长。
We prove a vector-valued almost sure invariance principle for some classes of time dependent non-uniformly distance expanding dynamical systems. The models we have in mind are certain sequential versions of the smooth non-uniformly distance expanding maps considered in \cite{castro} and \cite{Vara}, as well as certain types of sequences of covering maps. Our results rely on the theory of complex projective metrics which was developed in \cite{Rug}, together with the spectral methods of Gouëzel \cite{GO}. A big advantage in applying the theory of complex cones here is that it also yields additi…
We obtain a quenched vector-valued almost sure invariance principle (ASIP) for random expanding on average cocycles. This is achieved by combining the adapted version of Gouëzel's approach for establishing ASIP and the recent construction of the so-called adapted norms, which in some sense eliminate the non-uniformity of the decay of correlations. For real-valued observables, we also show that the martingale approximation technique is applicable in our setup, and that it yields the ASIP with better error rates. Finally, we present an example showing the necessity of a scaling condition, answer…
A Vector-Valued Almost Sure Invariance Principle for Hyperbolic Dynamical Systems
本文证明了大类非一致双曲动力系统的向量值Holder观测量的几乎必然不变原理（用d维布朗运动逼近）。这些系统包括Axiom~A同构和流以及具有中等尾部衰减率的Young塔模型系统。特别地，具有有限视界的平面周期洛伦兹气体的位置变量近似于二维布朗运动。
We prove a fiberwise almost sure invariance principle for random piecewise expanding transformations in one and higher dimensions using recent developments on martingale techniques.
Horseshoes for a class of nonuniformly expanding random dynamical systems on the circle
本文为一维随机动力系统引入随机马蹄概念，并证明在加性噪声足够大且李雅普诺夫指数为正时，一类圆周自同态中随机马蹄大量存在，其诱导动力学可实现两个符号上的全移位。
In this paper we show how to apply classical probabilistic tools for partial sums $\sum_{j=0}^{n-1}φ\circτ^j$ generated by a skew product $τ$, built over a sufficiently well mixing base map and a random expanding dynamical system. Under certain regularity assumptions on the observable $φ$, we obtain a central limit theorem (CLT) with rates, a functional CLT, an almost sure invariance principle (ASIP), a moderate deviations principle, several exponential concentration inequalities and Rosenthal type moment estimates for skew products with $α, ϕ$ or $ψ$ mixing base maps and expanding on the aver…
Given a piecewise $C^{1+β}$ map of the interval, possibly with critical points and discontinuities, we construct a symbolic model for invariant probability measures with nonuniform expansion that do not approach the critical points and discontinuities exponentially fast almost surely. More specifically, we code the lift of these measures in the natural extension of the map.
Given a rational map of the Riemann sphere and a subset $A$ of its Julia set, we study the $A$-exceptional set, that is, the set of points whose orbit does not accumulate at $A$. We prove that if the topological entropy of $A$ is less than the topological entropy of the full system then the $A$-exceptional set has full topological entropy. Furthermore, if the Hausdorff dimension of $A$ is smaller than the dynamical dimension of the system then the Hausdorff dimension of the $A$-exceptional set is larger than or equal to the dynamical dimension, with equality in the particular case when the dyn…
Wasserstein convergence rates in the invariance principle for nonuniformly hyperbolic flows
本文针对非一致双曲流，利用鞅-上边缘分解将离散时间方法推广到连续时间，得到了不变原理中q-Wasserstein收敛速率，并应用于Axiom A流、Young塔悬挂流及间歇螺线管流。
Almost sure mixing rates for non-uniformly expanding maps
考虑非一致扩张映射的随机扰动，可能具有非退化临界集。我们证明了，如果对于几乎所有的随机轨道，在某个时刻，非均匀展开或缓慢回归到临界集的点集的勒贝格测度都以指数形式衰减，那么在一定的等待时间内，沿随机轨道的相关性衰减也是指数形式的.作为应用，我们得到了Viana映射、一类非一致扩张局部自同态和二次区间映射族的随机相关的几乎必然拉伸指数衰减.
Almost sure invariance principle for sequential and non-stationary dynamical systems
我们建立了几乎必然不变原理，布朗运动的一种强形式的近似，对非平稳时间序列作为动力系统上的观察。我们的例子包括观测序列扩展映射，扰动动力系统，非平稳序列的功能，双曲系统以及应用程序的收缩目标问题的扩展系统。
We prove quenched versions of a central limit theorem, a large deviations principle as well as a local central limit theorem for expanding on average cocycles. This is achieved by building an appropriate modification of the spectral method for non-autonomous dynamics developed by Dragičević et al., to deal with the case of random dynamics that exhibits nonuniform decay of correlations, which are ubiquitous in the context of the multiplicative ergodic theory. Our results provide an affirmative answer to a question posed by Buzzi.
We provide a systematic approach for deducing statistical limit laws via martingale-coboundary decomposition, for nonuniformly hyperbolic systems with slowly contracting and expanding directions. In particular, if the associated return time function is square-integrable, then we obtain the central limit theorem, the weak invariance principle, and an iterated version of the weak invariance principle.
Gouezel and Sarig introduced operator renewal theory as a method to prove sharp results on polynomial decay of correlations for certain classes of nonuniformly expanding maps. In this paper, we apply the method to planar dispersing billiards and multidimensional nonMarkovian intermittent maps.
Statistical properties of coupled expanding maps on a lattice with general infinite range couplings and Hölder densities
我们继续发展的转移算子技术扩展映射的晶格耦合一般的相互作用函数。我们得到了一个适当定义的转移算子的谱隙，作为推论，系统的不变共形概率测度的存在性，相关性的指数衰减，中心极限定理和几乎必然的不变原理。
We consider deterministic homogenization (convergence to a stochastic differential equation) for multiscale systems of the form \[ x_{k+1} = x_k + n^{-1} a_n(x_k,y_k) + n^{-1/2} b_n(x_k,y_k), \quad y_{k+1} = T_n y_k, \] where the fast dynamics is given by a family $T_n$ of nonuniformly expanding maps. Part 1 builds on our recent work on martingale approximations for families of nonuniformly expanding maps. We prove an iterated weak invariance principle and establish optimal iterated moment bounds for such maps. (The iterated moment bounds are new even for a fixed nonuniformly expanding map T.)…
We extend the spectral approach of S. Gouëzel for the vector-valued almost sure invariance principle (ASIP) to certain classes of non-stationary sequences with a weaker control over the behavior of the covariance matrices, assuming only linear growth. Then we apply this extension to obtain a quenched vector-valued ASIP for random perturbations of a fixed Anosov diffeomorphism as well as random perturbations of a billiard map associated to the periodic Lorentz gas. We also consider certain classes of random piecewise expanding maps.
We prove results on mixing and mixing rates for toral extensions of nonuniformly expanding maps with subexponential decay of correlations. Both the finite and infinite measure settings are considered. Under a Dolgopyat-type condition on nonexistence of approximate eigenfunctions, we prove that existing results for (possibly nonMarkovian) nonuniformly expanding maps hold also for their toral extensions.
We prove vector-valued almost sure invariance principle (VASIP) for nonstationary dynamical systems, under assumptions of correlation decay and variance growth. Applications include VASIP for non-stationary (non)uniformly expanding dynamical systems, quenched VASIP for random dynamical systems. In particular, VASIP is satisfied for corresponding stationary dynamical systems.
A coupling approach to random circle maps expanding on the average
我们研究的是平均膨胀的随机圆图。膨胀和变形都不需要统一的界限。我们构造了一个耦合方案，它导致指数收敛的措施（记忆损失）和指数混合。利用相关估计的结构，我们证明了向量值观测量的几乎必然不变原理。我们的论文的动机是在非均匀随机设置中探索这些方法。
We obtain large and moderate deviation estimates, as well as concentration inequalities, for a class of nonuniformly expanding maps with stretched exponential decay of correlations. In the large deviation regime, we also exhibit examples showing that the obtained upper bounds are essentially optimal.
Improved polynomial rates of memory loss for nonstationary intermittent dynamical systems
本文研究非平稳间歇动力系统，在首返回时间尾部多项式衰减非一致的条件下，证明了尖锐的多项式记忆损失速率，并应用于Pomeau–Manneville型间歇映射及无界导数间歇映射的随机遍历复合。
Correlation decay and recurrence estimates for some robust nonuniformly hyperbolic maps
研究了一类稳健的多维非一致双曲变换的相关性衰减、首中时的渐近分布和返回时的涨落. Oliveira和Viana [15]证明了一大类非一致膨胀变换和具有小变化的Holder连续势存在唯一的平衡态。对于一类开的小变差位势，证明了Ruelle-Perron-Frobenius算子在本质有界变差函数空间$V_θ$中的拟紧性，其中函数空间严格包含Holder连续观测量.我们推导出平衡态具有指数衰减的关联。此外，我们还证明了首中时的指数渐近分布和返回时间围绕度量熵给出的平均值的对数正态波动。
Some almost sure results for unbounded functions of intermittent maps and their associated Markov chains
本文考虑了[0，1]中一类具有中性不动点的分段扩张映射T及其相应的马尔可夫链Y_i，其转移核是T关于绝对连续不变概率测度的Perron-Frobenius算子.本文给出了一类无界函数f的部分和f \circ T^i同时满足中心极限定理和有界重对数律.对于同一类，我们证明了f（Y_i）的部分和满足一个强不变原理.当类较大时，使得f \circ T^i的部分和可能属于指数为p \in（1，2）的稳定律的正规吸引域，我们证明了在强大数律中的几乎必然收敛速度与相应的i.i.d.案子
An almost sure ergodic theorem for quasistatic dynamical systems
本文证明了一类称为准静态动力系统的系统的几乎必然遍历定理。这些结果是必要的，因为通常的定理由于伯克霍夫不适用于不变测度的情况下。我们还引入了准静态动力系统的物理测度族的概念。例如，这些对象在数值实验中表现出来。然后，我们验证了定理的条件，并确定两个具体的模型，准静态扩展系统和准静态分散台球的措施的物理家庭。
We give a review of results on superpolynomial decay of correlations, and polynomial decay of correlations for nonuniformly expanding semiflows and nonuniformly hyperbolic flows. A self-contained proof is given for semiflows. Results for flows are stated without proof (the proofs are contained in separate joint work with Balint and Butterley). Applications include intermittent solenoidal flows, suspended Henon attractors, Lorenz attractors, and various Lorentz gas models including the infinite horizon Lorentz gas.
Law of iterated logarithm and invariance principle for one-parameter families of interval maps
我们证明了对于横截单参数单峰映射族中的几乎每一个映射，沿转向点前向轨道的适当观测量的Birkhoff和满足重对数重对数律.这个结果将遵循Birkhoff和作为参数空间上的函数的几乎必然的不变原理。此外，对于区间上一般的单参数分段扩张映射族，我们也得到了类似的结果。
Non-uniform specification and large deviations for weak Gibbs measures
我们建立了与连续观测值相关的偏差集的测量界限，这些连续观测值不一定是不变的弱吉布斯测度。在适当的假设下，得到了一些非一致扩张映射，包括二次映射和鲁棒多维非一致扩张局部自同态的偏差集测度的上界和下界.为此目的，一个测度理论的弱形式的规格介绍，并证明了持有的多维非一致扩展的局部同构和维亚纳映射的鲁棒类。
In this paper we deal with a large class of dynamical systems having a version of the spectral gap property. Our primary class of systems comes from random dynamics, but we also deal with the deterministic case. We show that if a random dynamical system has a fiberwise spectral gap property as well as an exponential decay of correlations in the base, then, developing on Gouëzel's approach, the system satisfies the almost sure invariance principle. The result is then applied to uniformly expanding random systems like those studied by Denker and Gordin and Mayer, Skorulski, and Urbański.
Explicit conditions for the CLT and related results for non-uniformly partially expanding random dynamical systems via effective RPF rates
该研究为非一致部分扩张的非独立同分布随机变换与随机Gibbs测度构成的系统提供了首类CLT及相关渐近结果的显式充分条件，证明了对应随机Birkhoff和满足多项概率极限定理。
Annealed and quenched limit theorems for random expanding dynamical systems
本文研究了随机膨胀动力系统的退火和淬火极限定理。利用泛函分析技术和更多的概率参数与鞅，我们证明了退火版本的中心极限定理，大偏差原理，局部极限定理，几乎必然不变原理。我们还讨论了猝灭的中心极限定理、动力学Borel-Cantelli引理、Erdös-Rényi定律和浓度不等式。
Rates of convergence in CLT and ASIP for sequences of expanding maps
本文针对扩张映射序列驱动的部分和，建立了带收敛速率的Berry-Esseen定理与几乎必然不变原理，并将结果推广到Axiom A映射小邻域及Hölder连续函数情形。
We consider partially hyperbolic \( C^{1+} \) diffeomorphisms of compact Riemannian manifolds of arbitrary dimension which admit a partially hyperbolic tangent bundle decomposition \( E^s\oplus E^{cu} \). Assuming the existence of a set of positive Lebesgue measure on which \( f \) satisfies a weak nonuniform expansivity assumption in the centre~unstable direction, we prove that there exists at most a finite number of transitive attractors each of which supports an SRB measure. As part of our argument, we prove that each attractor admits a Gibbs-Markov-Young geometric structure with integrable…
Convergence to decorated Lévy processes in non-Skorohod topologies for dynamical systems
该研究提出确定性系统向量值过程向装饰Lévy过程弱收敛的通用框架，适用于多类映射系统，弥补了Skorohod等拓扑无法捕捉漂移细节、不适用部分场景的局限。
We give conditions under which nonuniformly expanding maps exhibit lower bounds of polynomial type for the decay of correlations and for a large class of observables. We show that if the Lasota-Yorke type inequality for the transfer operator of a first return map are satisfied in a Banach space B, and the absolutely continuous invariant measure obtained is weak mixing, in terms of aperiodicity, then under some renewal condition, the maps have polynomial decay of correlations for observables in B. We also provide some general conditions that give aperiodicity for expanding maps in higher dimens…
We obtain the first results on convergence rates in the Prokhorov metric for the weak invariance principle (functional central limit theorem) for deterministic dynamical systems. Our results hold for uniformly expanding/hyperbolic (Axiom A) systems, as well as nonuniformly expanding/hyperbolic systems such as dispersing billiards, Henon-like attractors, Viana maps and intermittent maps. As an application, we obtain convergence rates for deterministic homogenization in multiscale systems.
Gibbs-Markov structures and limit laws for partially hyperbolic attractors with mostly expanding central direction
本文考虑黎曼流形$M$上的部分双曲集$K$，其切空间分裂为$T_K M=E^{cu}\oplus E^{s}$，中心不稳定方向$E^{cu}$在局部不稳定圆盘上非一致展开.我们表明，在这些假设下，$f$诱导吉布斯-马尔可夫结构。此外，返回时间函数的衰减可以根据典型点在中心不稳定方向上实现某种均匀扩展行为所需的时间来控制。作为主要结果的应用，我们得到了相关衰减的某些速率，大偏差，几乎必然不变原理和中心极限定理的有效性。
We prove statistical limit laws for sequences of Birkhoff sums of the type $\sum_{j=0}^{n-1}v_n\circ T_n^j$ where $T_n$ is a family of nonuniformly hyperbolic transformations. The key ingredient is a new martingale-coboundary decomposition for nonuniformly hyperbolic transformations which is useful already in the case when the family $T_n$ is replaced by a fixed transformation $T$, and which is particularly effective in the case when $T_n$ varies with $n$. In addition to uniformly expanding/hyperbolic dynamical systems, our results include cases where the family $T_n$ consists of intermittent …
We obtain quenched almost sure invariance principle (with convergence rate) for Random Young Tower. We apply our result to i.i.d perturbations of non-uniformly expanding maps. In particular, we answer one open question in \cite{BBM}.
Strong-Winning Target Avoidance for Manneville--Pomeau Maps
证明Manneville-Pomeau映射的目标回避集在Schmidt博弈中是强赢的，通过有限分支扩张映射逼近无限分支诱导映射并传递策略。
扫码添加微信好友，提出您的宝贵建议 👇
💡 备注请填写：网站反馈
发表机构由 AI 从论文文本抽取，如发现错误，欢迎反馈修正建议。