Stably non-synchronizable maps of the plane

$\u2164^2$上映射的非一致双曲性

Non-uniform hyperbolicity of maps on $\mathbb{T}^2$

该研究在二维环面线性自同态的两类同伦类中构造出非一致双曲映射，还得到带稳定遍历性的结果，部分回应了已有文献中的相关问题。

体积保持3维阿诺索夫流的时间-1映射的扰动

Perturbation of the time-1 map of a generic volume-preserving $3$-dimensional Anosov flow

研究在C^s拓扑下接近体积保持3维阿诺索夫流时间-1映射的微分同胚，证明其动力学性质，包括混合性、唯一物理测度及无周期点的示例。

Homotopical Dynamics: Suspension and Duality

Flow type suspension and homotopy suspension agree for attractor-repellor homotopy data.The connection maps associated in Conley index theory to an attractor-repellor decomposition with respect to the direct flow and its inverse are Spanier-Whitehead duals in the stably parallelizable context and are duals modulo a certain Thom construction in general.

On the fractional susceptibility function of piecewise expanding maps

We associate to a perturbation $(f_t)$ of a (stably mixing) piecewise expanding unimodal map $f_0$ a two-variable fractional susceptibility function $Ψ_ϕ(η, z)$, depending also on a bounded observable $ϕ$. For fixed $η\in (0,1)$, we show that the function $Ψ_ϕ(η, z)$ is holomorphic in a disc $D_η\subset \mathbb{C}$ centered at zero of radius $>1$, and that $Ψ_ϕ(η, 1)$ is the Marchaud fractional derivative of order $η$ of the function $t\mapsto \mathcal{R}_ϕ(t):=\int ϕ(x)\, dμ_t$, at $t=0$, where $μ_t$ is the unique absolutely continuous invariant probability measure of $f_t$. In addition, we s…

Stabilizing Embedology: Geometry-Preserving Delay-Coordinate Maps

Delay-coordinate mapping is an effective and widely used technique for reconstructing and analyzing the dynamics of a nonlinear system based on time-series outputs. The efficacy of delay-coordinate mapping has long been supported by Takens' embedding theorem, which guarantees that delay-coordinate maps use the time-series output to provide a reconstruction of the hidden state space that is a one-to-one embedding of the system's attractor. While this topological guarantee ensures that distinct points in the reconstruction correspond to distinct points in the original state space, it does not ch…