Grzegorz Swiatek
It is shown that for non-hyperbolic real quadratic polynomials topological and quasisymmetric conjugacy classes are the same. By quasiconformal rigidity, each class has only one representative in the quadratic family, which proves that hyperbolic maps are dense.
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
We present an infinite dimensional Banach space in which the set of hyperbolic linear isomorphisms in that space is not dense (in the norm topology) in the set of linear isomorphisms.
A note on the hyperbolicity of the non-wandering sets of real quadratic maps
本文针对实二次映射在参数接近-2时的非游荡集，给出两种证明其双曲性的方法，虽结果非新，但提供了更易获取的证明途径。
We prove that for a polynomial diffeomorphism of C^2, uniform hyperbolicity on the set of saddle periodic points implies that saddle points are dense in the Julia set. In particular f satisfies Smale's Axiom A on C^2 .
On the Non-Uniform Hyperbolicity of the Kontsevich-Zorich Cocycle for Quadratic Differentials
本文证明来自不可定向二次微分双重覆盖的阿贝尔微分上 Kontsevich-Zorich 上循环的非一致双曲性，并应用于典型叶同调偏差与遍历平均偏差的研究。
Using quadratic forms, we stablish a criteria to relate the curvature of a Riemannian manifold and partial hyperbolicity of its geodesic flow. We show some examples which satisfy the criteria and another which does not satisfy it but still has a partially hyperbolic geodesic flow.
We prove here that in the complement of the closure of the hyperbolic surface diffeomorphisms, the ones exhibiting a homoclinic tangency are C^1 dense. This represents a step towards the global understanding of dynamics of surface diffeomorphisms.
We prove that any diffeomorphism of a compact manifold can be approximated in topology C1 by another diffeomorphism exhibiting a homoclinic bifurcation (a homoclinic tangency or a heterodimensional cycle) or by one which is essentially hyperbolic (it has a finite number of transitive hyperbolic attractors with open and dense basin of attraction).
Let H be an infinite dimensional separable Hilbert space, X a compact Hausdorff space and f : X \rightarrow X a homeomorphism which preserves a Borel ergodic measure which is positive on non-empty open sets. We prove that the non-uniformly Anosov cocycles are C0-dense in the family of partially hyperbolic f,H-skew products with non-trivial unstable bundles.
In [15] the authors proved the Pugh-Shub conjecture for partially hyperbolic diffeomorphisms with 1-dimensional center, i.e. stable ergodic diffeomorphism are dense among the partially hyperbolic ones. In this work we address the issue of giving a more accurate description of this abundance of ergodicity. In particular, we give the first examples of manifolds in which all conservative partially hyperbolic diffeomorphisms are ergodic.
We study the bifurcation loci of quadratic (and unicritical) polynomials and exponential maps. We outline a proof that the exponential bifurcation locus is connected; this is an analog to Douady and Hubbard's celebrated theorem that (the boundary of) the Mandelbrot set is connected. For these parameter spaces, a fundamental conjecture is that hyperbolic dynamics is dense. For quadratic polynomials, this would follow from the famous stronger conjecture that the bifurcation locus (or equivalently the Mandelbrot set) is locally connected. It turns out that a formally slightly weaker statement is …
Hyperbolicity for one-frequency analytic quasi-periodic (Hermitian)-symplectic cocycles
本研究针对实解析单频拟周期Sp(4,R)-上循环类，证明存在以李雅普诺夫指数互异或加速度非零为特征的开稠子集，部分解答了A. Avila提出的公开问题。
Singular hyperbolicity is a weakened form of hyperbolicity that has been introduced for vector fields in order to allow non-isolated singularities inside the non-wandering set. A typical example of a singular hyperbolic set is the Lorenz attractor. However, in contrast to uniform hyperbolicity, singular hyperbolicity does not immediately imply robust topological properties, such as the transitivity. In this paper, we prove that open and densely inside the space of $C^1$ vector fields of a compact manifold, any singular hyperbolic attractors is robustly transitive.
In this work we obtain a new criterion to establish ergodicity and non-uniform hyperbolicity of smooth measures of diffeomorphisms. This method allows us to give a more accurate description of certain ergodic components. The use of this criterion in combination with topological devices such as blenders lets us obtain global ergodicity and abundance of non-zero Lyapunov exponents in some contexts. In the partial hyperbolicity context, we obtain that stably ergodic diffeomorphisms are C^1-dense among volume preserving partially hyperbolic diffeomorphisms with two-dimensional center bundle. This …
We study the specification property for partially hyperbolic dynamical systems. In particular, we show that if a partially hyperbolic diffeomorphism has two saddles with different indices, and stable manifold of one of them coincides with the strongly stable leaf, then it does not satisfy the specification property. As an application, we prove that there exists a $C^1$-open and dense subset $\mathcal P$ in the set of robustly non-hyperbolic transitive diffeomorphisms on a three dimensional closed manifold such that diffeomorphisms in $\mathcal P$ do not satisfy the specification property.
We prove that a C2 Hamiltonian system H in M is globally hyperbolic if any of the following statements holds: H is robustly topologically stable; H is stably shadowable; H is stably expansive; and H has the stable weak specification property. Moreover, we prove that, for a C2-generic Hamiltonian H, the union of the partially hyperbolic regular energy hypersurfaces and the closed elliptic orbits, forms a dense subset of M. As a consequence, any robustly transitive regular energy hypersurface of a C2-Hamiltonian is partially hyperbolic. Finally, we prove that stably weakly shadowable regular ene…
We prove uniform hyperbolicity of the renormalization operator for all possible real combinatorial types. We derive from it that the set of infinitely renormalizable parameter values in the real quadratic family $P_c: x\mapsto x^2+c$ has zero measure. This yields the statement in the title (where ``regular'' means to have an attracting cycle and ``stochastic'' means to have an absolutely continuous invariant measure). An application to the MLC problem is given.
We use hyperbolicity of golden-mean renormalization of dissipative Hénon-like maps to prove that the boundaries of Siegel disks of sufficiently dissipative quadratic complex Hénon maps with golden-mean rotation number are topological circles. Conditionally on an appropriate renormalization hyperbolicity property, we derive the same result for Siegel disks of Hénon maps with all eventually periodic rotation numbers.
A vector field X is called a star flow if every periodic orbit, of any vector field C1-close to X, is hyperbolic. It is known that the chain recurrence classes of a generic star flow X on a 3 or 4 manifold are either hyperbolic or singular hyperbolic (see [MPP] for 3-manifolds and [GLW] on 4-manifolds). As it is defined, the notion of singular hyperbolicity forces the singularities in the same class to have the same index. However, in higher dimension (i.e $\geq 5$) \cite{BdL} shows that singularities of different indices may be robustly in the same chain recurrence class of a star flow. There…
Joint typical periodic optimization: systems with stable hyperbolicity
本文研究了具有稳定双曲性的系统，提出了一个更广泛的联合扰动框架，并为几种重要的自然家庭建立了新的联合典型周期优化结果。
The famous MLC Conjecture states that the Mandelbrot set is locally connected, and it is considered by many to be the central conjecture in one-dimensional complex dynamics. Among others, it implies density of hyperbolicity in the quadratic family $\{z^2+c\}_{c\in\mathbb{C}}$. We describe recent advances on MLC and the relations between MLC, the Density of Hyperbolicity Conjecture, the Rigidity Conjecture, the No Invariant Line Fields Conjecture, and the Triviality of Fibers Conjecture. We treat families of unicritical polynomials and rational maps as well as the exponential family and familie…
Computable conditions for the occurrence of non-uniform hyperbolicity in families of one-dimensional maps
基于可计算初始条件，提出并证明了Jakobson-Benedicks-Carleson型定理，给出非一致双曲性（随机动力学）发生的显式可计算下界，并应用于二次族，证明绝对连续不变概率测度对应的参数集测度至少为10^{-5000}。
In this paper we revisit uniformly hyperbolic basic sets and the domination of Oseledets splittings at periodic points. We prove that periodic points with simple Lyapunov spectrum are dense in non-trivial basic pieces of Cr-residual diffeomorphisms on three-dimensional manifolds (r >= 1). In the case of the C1-topology we can prove that either all periodic points of a hyperbolic basic piece for a diffeomorphism f have simple spectrum C1- robustly (in which case f has a finest dominated splitting into one-dimensional sub-bundles and all Lyapunov exponent functions of f are continuous in the wea…
We prove the uniform hyperbolicity of the near-parabolic renormalization operators acting on an infinite-dimensional space of holomorphic transformations. This implies the universality of the scaling laws, conjectured by physicists in the 70's, for a combinatorial class of bifurcations. Through near-parabolic renormalizations the polynomial-like renormalizations of satellite type are successfully studied here for the first time, and new techniques are introduced to analyze the fine-scale dynamical features of maps with such infinite renormalization structures. In particular, we confirm the rig…
We study the $C^1$-topological properties of the subset of non-uniform hyperbolic diffeomorphisms in a certain class of $C^2$ partially hyperbolic symplectic systems which have bounded $C^2$ distance to the identity. In this set, we prove the stability of non-uniform hyperbolicity as a function of the diffeomorphism and the measure, and the existence of an open and dense subset of continuity points for the center Lyapunov exponents. These results are generalized to the volume-preserving context.
The long-standing problem of existence of nowhere dense rational Julia set with positive area has been solved by an example in quadratic polynomials by Buff and Chéritat. Since then many efforts have been devoted to finding out new classes of rational maps with nowhere dense Julia sets having positive area. So far, all known examples of this kind are renormalizable with only one exception which is a quadratic polynomial. In this paper, by developing a new approach, we prove that there exists a non-renormalizable cubic polynomial having a Julia set with positive area.
Difference sets in Quadratic Density Hales Jewett conjecture with 2 letters
本文研究2字母二次密度 Hales Jewett 猜想，证明稠密子集中存在差集为γ_1×γ_2的两个元素，并给出通配符集合受大小和形状限制的稠密向量子空间例子。
Density of orbits of horocycle flows at sub-quadratic polynomial times
本文证明非紧齐性空间上水平流在次二次多项式时间（如 $n^{2-\delta}$）及素数时间下的轨道稠密性，并在模群情形给出平方时间周期点轨道的等分布结果。
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。