Computation of Topological Entropy via $ϕ$-expansion, an Inverse Problem for the Dynamical Systems $βx+α\mod 1$

Entropy of homeomorphisms on unimodal inverse limit spaces

We prove that every self-homeomorphism $h : K_s \to K_s$ on the inverse limit space $K_s$ of the tent map $T_s$ with slope $s \in (\sqrt 2, 2]$ has topological entropy $\htop(h) = |R| \log s$, where $R \in \Z$ is such that $h$ and $σ^R$ are isotopic. Conclusions on the possible values of the entropy of homeomorphisms of the inverse limit space of a (renormalizable) quadratic map are drawn as well.

Topological entropy of diagonal maps on inverse limit spaces

We give an upper bound for the topological entropy of maps on inverse limit spaces in terms of their set-valued components. In a special case of a diagonal map on the inverse limit space $\underleftarrow{\lim}(I,f)$, where every diagonal component is the same map $g\colon I\to I$ which strongly commutes with $f$ (i.e. $f^{-1}\circ g=g\circ f^{-1}$), we show that the entropy equals $\max\{\textrm{Ent}(f),\textrm{Ent}(g)\}$. As a side product, we develop some techniques for computing topological entropy of set-valued maps.

自同态的局部逆测度熵

Local inverse measure-theoretic entropy for endomorphisms

本文提出自同态遍历测度的局部逆测度熵概念，证明其等于正向熵减折叠熵，并用于自同态分类、熵刚性及变分原理，最后计算了多类自同态 SRB 测度的局部逆熵。

面向XDE反问题的熵结构引导学习

Entropy Structure Informed Learning for Inverse XDE Problems

本研究提出一种利用熵平衡方程求解XDE反问题的新方法，经多类算例验证，该方法准确可靠，性能与经典方法SINDy相当。

Analysis of relationships between spectral potential of transfer operators, $t$-entropy, entropy and topological pressure

The paper is devoted to the analysis of relationships between principal objects of the spectral theory of dynamical systems (transfer and weighted shift operators) and basic characteristics of information theory and thermodynamic formalism (entropy and topological pressure). We present explicit formulae linking these objects with $t$-entropy and spectral potential. Herewith we uncover the role of inverse rami-rate, forward entropy along with essential set and the property of non-contractibility of a dynamical system.

$C^{1+α}$映射的折叠型熵公式

Entropy formula of folding type for $C^{1+α}$ maps

本文针对一般$C^{1+α}$映射（含零Jacobian退化情形）建立了折叠型熵公式，证明测度为逆SRB测度当且仅当该公式成立且Jacobian级数可积，为此发展了相应的Pesin理论。