Marco Martens, Welington de Melo
It will be shown that the smooth conjugacy class of an $S-$unimodal map which does not have a periodic attractor neither a Cantor attractor is determined by the multipliers of the periodic orbits. This generalizes a result by M.Shub and D.Sullivan for smooth expanding maps of the circle.
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 consider a space of complex polynomials of degree $n\ge 3$ with $n-1$ distinguished periodic orbits. We prove that the multipliers of these periodic orbits considered as algebraic functions on that space, are algebraically independent over the field of complex numbers.
We present the following result: consider the space of complex polynomials of degree n>2 with n-1 distinct marked periodic orbits of given periods. Then this space is irreducible and the multipliers of the marked periodic orbits considered as algebraic functions on the above mentioned space, are algebraically independent over $\mathbb C$. Equivalently, this means that at its generic point, the moduli space of degree n polynomial maps can be locally parameterized by the multipliers of n-1 arbitrary distinct periodic orbits. A detailed proof of this result (together with a proof of a more genera…
We consider the space of degree $n\ge 2$ rational maps of the Riemann sphere with $k$ distinct marked periodic orbits of given periods. First, we show that this space is irreducible. For $k=2n-2$ and with some mild restrictions on the periods of the marked periodic orbits, we show that the multipliers of these periodic orbits, considered as algebraic functions on the above mentioned space, are algebraically independent over $\mathbb C$. Equivalently, this means that at its generic point, the moduli space of degree $n$ rational maps can be locally parameterized by the multipliers of any $2n-2$ …
Periodic Solutions of a Delay Differential Equation with a Periodic Multiplier
本文研究带周期乘子的时滞非自治标量微分方程，证明存在两类稳定慢振荡周期解，分段常数情形下可显式构造，且小光滑扰动下周期动力学可保持，结果经数值模拟验证。
We give a lower bound for the multipliers of repelling periodic points of entire functions. The bound is deduced from a bound for the multipliers of fixed points of composite entire functions.
We discuss tangent maps related to the multipliers of periodic points of a typical one-dimensional polynomial map.
We prove that there is no entire transcendental function in class S with real multipliers of all repelling periodic orbits.
Blow-up of multipliers in meromorphic families of rational maps
本文研究了黎曼球面上有理映射的单参数全纯退化族中周期循环乘子的爆破现象。
Given a polynomial or a rational map f we associate to it a space of maps. We introduce local coordinates in this space, which are essentially the set of critical values of the map. Then we consider an arbitrary periodic orbit of f with multiplier ρ\not=1 as a function of the local coordinates, and establish a simple connection between the dynamical plane of f and the function ρin the space associated to f. The proof is based on the theory of quasiconformal deformations of rational maps. As a corollary, we show that multipliers of non-repelling periodic orbits are also local coordinates in the…
We prove that if the multipliers of the repelling periodic orbits of a complex polynomial grow at least like $n^{5 + ε}$, for some $ε> 0$, then the Julia set of the polynomial is locally connected when it is connected. As a consequence for a polynomial the presence of a Cremer cycle implies the presence of a sequence of repelling periodic orbits with "small" multipliers. Somehow surprinsingly the proof is based in measure theorical considerations.
We prove an extension results for the multiplier of an attracting periodic orbit of a quadratic map as a function of the parameter. This has applications to the problem of geometry of the Mandelbrot and Julia sets. In particular, we prove that the size of p/q-limb of a hyperbolic component of the Mandelbrot set of period n is O(4^n/p), and give an explicit condition on internal arguments under which the Julia set of corresponding (unique) infinitely renormalizable quadratic polynomial is not locally connected
We consider cubic polynomials f(z)=z^3+az+b defined over the function field C(L), with a marked point of period N and multiplier L. In the case N=1, there are infinitely many such objects, and in the case N>2, only finitely many. The case N=2 has particularly rich structure, and we are able to describe all such cubic polynomials defined over the field obtained by adjoining to C the mth roots of L, for all L.
Dynamical Systems of Correspondences on the Projective Line II: Degrees of Multiplier Maps
本文研究乘子反问题，给出等谱对应数量的显式上界，并以两种计算方法证明 Hutz-Tepper 关于一般三次态射乘子唯一性结果的勘误修正。
A parameter $c_0\in\mathbb C$ in the family of quadratic polynomials $f_c(z)=z^2+c$ is a critical point of a period $n$ multiplier, if the map $f_{c_0}$ has a periodic orbit of period $n$, whose multiplier, viewed as a locally analytic function of $c$, has a vanishing derivative at $c=c_0$. We prove that all critical points of period $n$ multipliers equidistribute on the boundary of the Mandelbrot set, as $n\to\infty$.
Independence of multipliers via degenerations of rational maps
本文通过有理映射的退化方法，证明次数为$d$的有理映射中任意$2d-2$个不同周期轨道的乘子代数独立，条件为至多$d$个不动点，并改进了早期结果。
Multi-winged Lorenz attractors due to bifurcations of a periodic orbit with multipliers $(-1,i,-i)$
本文通过研究乘子为 $(-1,i,-i)$ 的周期轨道分岔，在三维二次 Hénon 映射中发现了三种伪双曲类 Lorenz 吸引子，包括经典 Lorenz 吸引子的离散对应物以及新的双翼和四翼 Simó 天使，并确定了它们存在的参数开区域。
The lunar periods of our moon -- the companion of the Earth -- which date back to the Babylonians until around 600 BCE, are 29.53 days for the synodic, 27.55 days for the anomalistic and 27.21 days for the draconitic month. In this paper we define and compute these periods in terms of Floquet multipliers and Conley--Zehnder indices for planar periodic orbits in the spatial Hill lunar problem, which is a limit case of the spatial circular restricted three body problem. For very low energies, we are able to prove analytically the existence of the families of planar direct (family $g$) and retrog…
Morse Index, Stability and Spectral Bounds for Periodic Orbits in Reversible Lagrangian Systems
本文针对可逆拉格朗日系统，利用莫尔斯指标与狄利克雷指标给出周期轨道弗洛凯乘子的定量谱界，证明指标一刹车轨道的横向双曲性，并展示精细界的尖锐性。
The multiplier spectrum morphism is generically injective
本文证明射影直线上有理映射模空间中的乘子谱态射除柔性 Lattès 族外在一般情形下是单射，从而加强了 McMullen 的拟有限性定理，并回答了 McMullen 与 Poonen 的问题。
Homoclinic orbits, multiplier spectrum and rigidity theorems in complex dynamics
本文利用复动力学与非阿基米德动力学工具，给出 McMullen 乘子谱刚性定理的新证明，并将其推广到长度谱情形，同时解决 Milnor 关于例外映射的两个猜想。
A parameter $c_0\in\mathbb C$ in the family of quadratic polynomials $f_c(z)=z^2+c$ is a critical point of a period $n$ multiplier, if the map $f_{c_0}$ has a periodic orbit of period $n$, whose multiplier, viewed as a locally analytic function of $c$, has a vanishing derivative at $c=c_0$. We study the accumulation set $\mathcal X$ of the critical points of the multipliers, as $n\to\infty$. This study complements the equidistribution result for the critical points of the multipliers that was previously obtained by the authors. In particular, in the current paper we prove that the accumulation…
We develop an eigenvalue-based approach for the stability assessment and stabilization of linear systems with multiple delays and periodic coefficient matrices. Delays and period are assumed commensurate numbers, such that the Floquet multipliers can be characterized as eigenvalues of the monodromy operator and by the solutions of a finite-dimensional non-linear eigenvalue problem, where the evaluation of the characteristic matrix involves solving an initial value problem. We demonstrate that such a dual interpretation can be exploited in a two-stage approach for computing dominant Floquet mul…
In this article we will see some properties that guarantee that a product of an ergodic non-singular action and a probability preserving ergodic action is also an ergodic action. We will start by proving 'The multiplier theorem' for locally compact abelian groups. Then we will show that for certain locally compact Polish groups (Moore groups, and minimally weakly mixing groups), a non-singular G action is weakly mixing if and only if any finite dimensional G-invariant subspace of L_\infty is trivial. Finally, we will show that the Gaussian action associated to the infinite dimensional irreduci…
Critical points of the multiplier map for the quadratic family
研究二次族中周期为n的周期轨道乘数函数的临界点，提出计算该函数临界点的数值算法，并计算n=1到10的临界点。
Independence of multipliers in several variables complex dynamics
本文证明多变量复动力系统中 C^n 与 P^n 自同态乘子的独立性，并据此推广分支测度和临界高度结果。
A robotic system can be viewed as a collection of lower-dimensional systems that are coupled via reaction forces (Lagrange multipliers) enforcing holonomic constraints. Inspired by this viewpoint, this paper presents a novel formulation for nonlinear control systems that are subject to coupling constraints via virtual "coupling" inputs that abstractly play the role of Lagrange multipliers. The main contribution of this paper is a process---mirroring solving for Lagrange multipliers in robotic systems---wherein we isolate subsystems free of coupling constraints that provably encode the full-ord…
Distributions of periodic points for the Dyck shift and the heterochaos baker maps
本文证明了 Dyck 位移的两个最大熵遍历测度可表示为不同乘子周期点集的渐近分布，并将该结果推广到异混沌面包师映射，用不同不稳定维数刻画其两个最大熵遍历测度。
Symmetric solutions of the $n$-body problem: a numerical study of Floquet multipliers and Morse indices
本文研究n体问题中满足对称约束的周期解的稳定性，通过计算Floquet乘数和Morse指数来分析其稳定性特性。
In this paper we consider nonlinear Schrodinger systems with periodic boundary condition in high dimension. We establish an abstract infinite dimensional KAM theorem and apply it to the nonlinear Schrodinger equation systems with real Fourier Multiplier. By establishing a block-diagonal normal form, We prove the existence of a class of Whitney smooth small amplitude quasi-periodic solutions corresponding to finite dimensional invariant tori of an associated infinite dimensional dynamical system.
In this paper we consider a class of higher dimensional differential systems in $\mathbb R^n$ which have a two dimensional center manifold at the origin with a pair of pure imaginary eigenvalues. First we characterize the existence of either analytic or $C^\infty$ inverse Jacobian multipliers of the systems around the origin, which is either a center or a focus on the center manifold. Later we study the cyclicity of the system at the origin through Hopf bifurcation by using the vanishing multiplicity of the inverse Jacobian multiplier.
Generic reconstruction of rational maps from multipliers of periods one and two
本文证明对任意次数d≥2且特征非2的域，模空间上由周期一、二乘子构成的谱态射双有理于其像闭包，从而在代数闭域上通用单射，证实了Ji-Xie猜想，方法涉及正规形、非阿基米德退化与对不变量重构。
Multipliers for forced Lurye systems with slope-restricted nonlinearities
本文提出了一种用于具有斜率限制非线性的强迫Lurye系统的动态乘数方法，以保证系统的稳定性与有限的增量增益，并探讨了其在不同激励下的响应特性。
Rigidity in Complex Dynamics: Multiplier Spectrum and Dynamical André-Oort Conjecture
本研究介绍一维复动力学刚性问题的近期进展，证明了曲线的动力André-Oort猜想及乘子谱的一般单射性，其证明结合代数几何、Arakelov几何与复动力学思想。
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。