动力系统
We investigate the box dimension of the graphs of a class of continuous periodic functions $G_\delta(x)=\sum_{n=1}^{\infty}g(n^{2}x)n^{-1-\delta}$ with 1-periodic Lipschitz functions $g$ and $0<\delta\le 1$, which generalizes the result of…
This paper investigates the Hurwitz existence problem for rational maps with three branch points. We establish several new families of realizable branch data and identify previously undocumented exceptional data. This work constitutes the…
We prove that an action by $C^1$ diffeomorphisms of a lattice in a simple $p$-adic group on a compact manifold is finite, provided the dimension is less than the rank. We extend this statement to lattices in totally disconnected…
We study three-degree-of-freedom Hamiltonian systems that are invariant under rotations about the $z$-axis and under reflection across the $xy$-plane. Fixing the angular momentum, such systems reduce to Hamiltonian systems with two degrees…
Using a variational approach, we study the existence of periodic solutions with prescribed energy for the relativistic equation \begin{equation*} \dfrac{\mathrm{d}}{\mathrm{d}t}\left(\dfrac{m\dot x}{\sqrt{1-|\dot{x}|^{2}/c^{2}}}\right) =…
We extend the Susceptible--Addicted--Reformed (SAR) model of \cite{sanchez2023}, which exhibits a forward--backward bifurcation driven by nonlinear relapse, by embedding an epi-economic behavioral layer in the spirit of \cite{fenichel2011}.…
We study resonance phenomena in the periodically forced Suarez--Schopf delay differential equation, which is a conceptual climate model for the El Ni\~no--Southern Oscillation (ENSO). The system serves as a prototypical forced…
Hypergraphs encode rich multiway interactions, but not all structural information is equally accessible through the dynamics. By analyzing pattern-forming instabilities in reaction-diffusion systems on directed hypergraphs, this work…
We model an adaptive contest in which two antagonistically coupled populations continually reallocate effort among competing methods, but decisions are not fielded instantly. Each side has an intended portfolio and a deployed portfolio:…
In this paper, we introduce the concept of block sub-additive potential. The topological and measure-theoretic pressures are then defined for the space of average pseudo-orbits relative to any block sub-additive potential and any open cover…
We study the symmetrical Dziobek configurations where, in $\mathbb{R}^{d}$, there are $d$ bodies with unit masses at the vertices of a regular $(d-1)$-dimensional simplex of unit edge length and two more bodies with nonzero masses $s,k$ are…
We show that there is no infinite spin at total collisions for $-\kappa$-homogeneous N-body problem in higher dimensional Euclidean space $\mathbb{R}^d$, in which $0 < \kappa < 2$ ($\kappa = 1$ the Newtonian case), provided the limiting…
We establish Extreme Value Distributions for the closest encounter between trajectories generated by different maps defined in the same reference phase space. For a class of strongly mixing maps, we show that the limit distribution depends…
Lyapunov exponents are fundamental invariants in smooth ergodic theory describing the asymptotic infinitesimal behavior along typical orbits. This text aims to explain how and why to control Lyapunov exponents using entropy for smooth…
We present some developments in the study of chaotic dynamics following the solution of a conjecture of Newhouse on the measures maximizing the entropy of smooth surface diffeomorphisms. We focus on \emph{strong positive recurrence}, a…
We study the compositionality of global dynamics through attractor lattices and order structures of recurrent dynamics in product and skew-product systems using Conley theory. For product systems, these structures can be characterized…
We prove a Nekhoroshev type result for a time quasiperiodic perturbation of an integrable Hamiltonian system. More precisely, we assume that the integrable part is analytic and fulfills a generic nondegeneracy condition introduced by…
We consider infinite-type IETs arising from elementary examples of finite-area translation surfaces of infinite genus such as the Baker's surface. We call such IETs tail-reversing and we show that for any tail-reversing permutation the…
A Pisot numeration system $U$ for $\mathbb N$ is a sequence of natural numbers generated by an integral homogeneous linear recurrence whose characteristic polynomial is the minimal polynomial of a Pisot number. The purpose of this paper is…
We study the existence of stable invariant measures for operators and strongly continuous semigroups of operators on Banach spaces admitting either a dense bilateral backward orbit or a sufficiently rich family of eigenvectors. These…