Topologically stable and $β$-persistent points of group actions

具有全不连通的朱利亚集的有理映射的非持续常回复点、qc-手术和不稳定性

Non-persistently recurrent points, qc-surgery and instability of rational maps with totally disconnected Julia sets

设$ R $是具有全不连通的朱利亚集$ J(R). $的有理映射.若$ J(R) $上的后临界集包含一个非持久递归（或锥）点，则证明了该映射$ R $不可能是结构稳定映射.

关于更高维度的马蹄形几何

On the geometry of horseshoes in higher dimensions

Moreira和Yoccoz引入了递归紧集的判据，证明了正则Cantor集在实直线上的稳定交在其豪斯多夫维数之和大于1的区域内是稠密的.我们适应这一概念的上下文马蹄周围的维度高于2，并证明了马蹄与上稳定维度大于1满足，通常和持续，适应标准的经常性紧集。作为后果，我们显示了这些马蹄铁的一些持久的几何性质。特别地，典型地且持续地，具有大于1的上稳定尺寸的马蹄形存在搅拌器。

On 2-diffeomorphisms with one-dimensional basic sets and a finite number of moduli

This paper is a step towards the complete topological classification of Ω-stable diffeomorphisms on an orientable closed surface, aiming to give necessary and sufficient conditions for two such diffeomorphisms to be topologically conjugate without assuming that the diffeomorphisms are necessarily close to each other. In this paper we will establish such a classification within a certain class Ψ of Ω-stable diffeomorphisms de- fined below. To determine whether two diffeomorphisms from this class Ψ are topologically conjugate, we give (i) an algebraic description of the dynamics on their non-tri…

关于二次多项式的朱利亚集的勒贝格测度

On the Lebesgue measure of the Julia set of a quadratic polynomial

本文的目的是证明以下定理：设$p_a(z) = z^2+a$是一个二次多项式，它没有无理的中立周期点，并且不是无限可重整的.则朱利亚集的$J(p_a)$的勒贝格测度等于零。作为证明的一部分，我们讨论了临界点是{ \it持续常返}的一个性质，并将我们的结果与实一维映射的相应结果联系起来.特别是，我们表明，在持续经常性的情况下，限制$p_a|ω(0)$是拓扑最小的，并有零拓扑熵。Douady-Hubbard-Yoccoz刚性定理遵循这个结果。

Stability Theorems for Group Actions on Uniform Spaces

We extend the notions of topological stability, shadowing and persistence from homeomorphisms to finitely generated group actions on uniform spaces and prove that an expansive action with either shadowing or persistence is topologically stable. Using the concept of null set of a Borel measure $μ$, we introduce the notions of $μ$-expansivity, $μ$-topological stability, $μ$-shadowing and $μ$-persistence for finitely generated group actions on uniform spaces and show that a $μ$-expansive action with either $μ$-shadowing or $μ$-persistence is $μ$-topologically stable.

Local Immunodeficiency: Role of Neutral Viruses

This paper analyzes the role of neutral viruses in the phenomenon of local immunodeficiency. We show that, even in the absence of altruistic viruses, neutral viruses can support the existence of persistent viruses, and thus local immunodeficiency. However, in all such cases neutral viruses can maintain only bounded (relatively small) concentration of persistent viruses. Moreover, in all such cases the state of local immunodeficiency could only be marginally stable, while it is known that altruistic viruses can maintain stable local immunodeficiency. We also present an absolutely minimal cross-…

二维紧集上的持久丛

Persistent bundles over a two dimensional compact set

紧致流形的$C^1$ -结构稳定的仿射是满足公理A和强横截条件（AS）的仿射.我们将AS的概念从非同态推广到不变紧子集。在其他性质中，我们显示的AS不变的紧集$K$的表面仿射$f$的结构稳定性。此外，如果$\hat f$是紧致流形的动力学，它在$f$上纤维化，使得丛在$f_{|K}$的非徘徊集上通常是双曲的，则$K$上的丛是持久的.这提供了通常不是双曲线的持久层积的非平凡例子。

Persistent homoclinic tangencies and infinitely many sinks for residual sets of automorphisms of low degree in C^{3}

We show that there exists a polynomial automorphism $f$ of $\mathbb{C}^{3}$ of degree 2 such that for every automorphism $g$ sufficiently close to $f$, $g$ admits a tangency between the stable and unstable laminations of some hyperbolic set. As a consequence, for each $d \ge 2$, there exists an open set of polynomial automorphisms of degree at most $d$ in which the automorphisms having infinitely many sinks are dense. To prove these results, we give a complex analogous to the notion of blender introduced by Bonatti and Diaz.

三维系统鸭式轨迹分析中的拓扑度

Topological degree in analysis of canard-type trajectories in 3-D systems

给出了非光滑慢-快系统存在拓扑稳定周期鸭式解的充分条件。

允许持久同步的耦合函数的一般理论

Towards a general theory for coupling functions allowing persistent synchronization

研究了具有类似扩散作用的耦合动力系统网络的同步性质。我们假设孤立节点动力学具有一个向前不变集，在该不变集上有一个有界雅可比矩阵，然后我们构造了一类耦合函数，它允许在连接的复杂网络中实现一致稳定的同步-在这个意义上，有一个开放的初始条件的邻域，它被一致地吸引向同步。此外，这种稳定的同步持续扰动下不相同的节点动态。我们用数值例子说明了理论，并得出结论，讨论嵌入这些结果在一个更一般的框架谱二分法。

利用持续同调稳定测量动力系统中的混沌

A Stable Measure of Chaos in Dynamical Systems using Persistent Homology

本文提出基于持续同调的0维持续指数作为混沌测量方法，证明其理论稳定性，并在洛伦茨和罗斯勒系统中验证其实验稳定性。