动力系统
This paper studies homothetic and more general weighted averages for flows. Absolutely continuous convolutions of singular weights are considered, thereby strengthening Kozlov-Treshchev's result on nonuniform averages for ergodic flows. The…
We introduce the notions of Fatou and Julia sets in the context of word maps on complex Lie groups and polynomial maps on finite-dimensional associative $\mathbb C$-algebras. For the group-theoretic question, we investigate the dynamics of…
We prove Liv\v{s}ic-type regularity results of coboundary representations for non-autonomous dynamical systems. Our results have an abstract nature and apply to several important specific situations, such as (higher-dimensional) random or…
We propose a compartmental model for epidemiology wherein the population is split into groups with either comply or refuse to comply with protocols designed to slow the spread of a disease. Parallel to the disease spread, we assume that…
We observe that a particular first integral of the partially-averaged system in the secular theory of the three-body problem appears also as an important conserved quantity of integrable Kepler billiards. In this note we illustrate their…
We present a characterization of $(\mu,\nu)$-dichotomies in terms of the admissibility of certain pairs of weighted spaces for nonautonomous discrete time dynamics acting on Banach spaces. Our general framework enables us to treat various…
We study the fine local scaling properties of a class of self-affine fractal sets called Gatzouras-Lalley carpets. More precisely, we establish a formula for the Assouad spectrum of all Gatzouras-Lalley carpets as the concave conjugate of…
In this work we study the backward filled Julia sets of a class of $p$-adic polynomial maps $f:\mathbb{Q}_p^2\longrightarrow \mathbb{Q}_p^2$ defined by $f(x,y)=(xy+c,x)$, where $c\in\mathbb{Q}_p$ is a $p$-adic number. In particular, if…
Understanding how the brain switches from normal activity to an epileptic seizure is essential for improving seizure therapy, yet the underlying mechanisms remain largely unknown. In particular, seizure onset can be described as a critical…
The port-Hamiltonian framework is a structure-preserving modeling approach that preserves key physical properties such as energy conservation and dissipation. When subsystems are modeled as port-Hamiltonian systems (pHS) with linearly…
This article proposes a nonlinear microscopic dynamical model for autonomous electric vehicles (A-EVs) that considers battery energy efficiency in the car-following dynamics. The model builds upon the Optimal Velocity Model (OVM), with the…
This paper studies regular topological flows $f^t$ defined on closed {topological} manifolds $M^n$. The chain recurrent set of such a flow consists of a finite number of topologically hyperbolic fixed points and periodic orbits. Like their…
Chaotic bursting behaviors have been observed by many authors in neural dynamics mainly in the transition between different kinds of bursting behavior. As a well-known three-dimensional ODEs model with various bursting solutions, the…
In 1986, Moser showed that for a given area-preserving map, there exists a Hamiltonian system that realizes it on the Poincar\'e section. Using his technique, we show that for any braid, there exists a Hamiltonian system whose orbits…
Let $f$ be a pseudo-Anosov homeomorphism on a closed, oriented surface. We give an effective construction of Markov partitions for $f$ based on a simple combinatorial criterion deciding when an immersed graph bounds a Markov partition. This…
Every pseudo-Anosov homeomorphism $f$ admits infinitely many Markov partitions. A \textit{geometric Markov partition} is a Markov partition $\mathcal{R}$ in which each rectangle is equipped with a vertical orientation. To each pair $(f,…
An isotopy between two diffeomorphisms means the existence of an arc connecting them in the space of diffeomorphisms. Among such arcs there are so-called stable arcs, which do not qualitatively change under small perturbations. In the…
We present a novel approach to modeling market dynamics using ordinary differential equations that explicitly incorporates product competitiveness and consumer behavior. Our framework treats market segments as interacting populations in a…
Numerical tests of volume formulae are presented to compute efficiently the volume enclosed between flux surfaces for integrable 3D vector fields with various degrees of symmetry. In the process, a new case is proposed and tested.
We study discrete-time dynamical systems that switch between different evolution rules based on thresholds that themselves adapt over time. Specifically, we analyze the coupled recursion $a_{n+1} = f(a_n)$ if $a_n \leq c_n$ and $a_{n+1} =…