动力系统

Differential-algebraic equations (DAEs) integrate ordinary differential equations (ODEs) with algebraic constraints, providing a fundamental framework for developing models of dynamical systems characterized by timescale separation,…

The main purpose of this paper is to strengthen our understanding of sofic mean dimension of two typical classes of sofic group actions. First, we study finite group actions. We prove that sofic mean dimension of any amenable group action…

We refine two results in the paper entitled "Sofic mean dimension" by Hanfeng Li, improving two inequalities with two equalities, respectively, for sofic mean dimension of typical actions. On the one hand, we study sofic mean dimension of…

For a class of Fibonacci-like unimodal maps, the restriction to the $\omega$-limit set of the unique turning point defines a minimal Cantor system. We construct these Cantor sets geometrically using a nested sequence of finite covers with a…

We show that, like cusps, horns in billiards expel every trajectory after finitely many collisions. We further produce an adiabatic invariant.

Many data-driven algorithms in dynamical systems rely on ergodic averages that converge painfully slowly. One simple idea changes this: taper the ends. Weighted Birkhoff averages can converge much faster (sometimes superpolynomially, even…

We construct geometrically infinite hyperbolic surfaces supporting horocycles with tailored recurrence properties. In particular, we obtain the first examples of non-trivial minimal horocyclic orbit closures and of infinite locally-finite…

We studied the transfer operators defined over $\mathbb{C}_p$-valued analytic functions for subhyperbolic rational maps on $\mathbb{Q}_p$, and showed that the corresponding Ruelle's zeta functions are meromorphic on $\mathbb{C}_p$. We also…

In this paper, we investigate the Hausdorff measure of planar dominated self-affine sets at their affinity dimension. We show that the Hausdorff measure being positive and finite is equivalent to the K\"aenm\"aki measure being a mass…

The goal of this work is to identify steady-state solutions to dynamical systems defined on large, random families of networks. We do so by passing to a continuum limit where the adjacency matrix is replaced by a non-local operator with…

The notion of relatedness loci in the parabolic slices Per_1(e^{2\pi i p/q}) in moduli space of quadratic rational maps is introduced. They are counterparts of the disconnectedness or escape locus in the slice of quadratic polynomials. A…

We introduce two families of infinite iterated function systems (IFSs) $\mathcal{F}(\mathbf{d}, T)$ and $\mathcal{G}(\mathbf{d}, T)$, parametrized by a sequence of positive real numbers $\mathbf{d}$ and a natural number $T$, and investigate…

This work focuses on the study of monodromic singularities in planar analytic families of vector fields whose Newton diagram consists of exactly two edges. We begin by analyzing the desingularization scheme of a minimal model of polynomial…

In this paper, we derive the Onsager--Machlup functional for a second-order Newton-type stochastic system driven by time-dependent fractional noise, \[ X_t'' = f_t(X_t, X_t') + \sigma_t \,\xi_t^{H}, \] where \( H \in (1/4,1) \). The…

This paper constructs a fast and effective novel numerical scheme which accurately calculates the dynamics of weakly-interacting pulses in the two-dimensional quintic-complex Ginzburg-Landau equation (QCGLE). The numerical scheme uses a…

This paper is about topological dynamics of cellular automata on finitely generated groups. We tackle the problem of determining for which group sensitivity to initial conditions is equivalent to the absence of equicontinuity points…

We confirm a conjecture posed by Bergelson, Moreira, and Richter (arXiv:1711.05729), and in particular show that for every probability measure preserving system $(X,\mathscr{B},\mu,T)$, every $k\in \mathbb{N}$, every set $A\in \mathscr{B}$…

For certain typical perturbations $(f_n)_n$ of a rational map $f$ with parabolic cycles, we investigate the relations between the Hausdorff convergence of Julia sets and invariant rays, and the horocyclic convergence of multipliers of…

Regime shifts in biology, ecology, and other complex systems are often interpreted through stability landscapes and early warning signals that implicitly assume dynamics without memory effects. Yet many real systems exhibit these effects,…

We prove that for two post-critically finite quadratic polynomials $f,g$, there is a mapping class $\phi$ of the sphere with finitely many marked points such that $f\phi$ and $g$ are pure Hurwitz equivalent.