动力系统

The sparse identification of nonlinear dynamics (SINDy) has been established as an effective method to learn interpretable models of dynamical systems from data. However, for high-dimensional slow-fast dynamical systems, the regression…

In this paper, we extend the concept of generalized entropy to uniform spaces, allowing computations beyond metrizable settings. We apply this to parabolic dynamics - systems with a unique fixed point uniformly attracting all compact…

This paper is devoted to study the equilibrium states for almost-additive potentials defined over topologically mixing countable Markov shifts (that is a non-compact space) without the big images and preimages (BIP) property. Let $\F$ be an…

In this paper, we study the holomorphic foliations admitting a common invariant algebraic set $C$ defined by a polynomial $f$ in $ \mathbb{K}[x_1,x_2,...,x_n]$ over any characteristic $0$ subfield $\mathbb{K}\subseteq\mathbb{C}$. For the…

We establish the existence and finiteness of equilibrium states for a class of partially hyperbolic endomorphisms. In our first result, we assume that the central direction is simple. In the second result, we consider the case where there…

We introduce two abstract constructions for building new measurable dynamical systems from existing ones and study their ergodic properties. The first of these constructions, a "reciprocal transformation," produces a type of non-singular…

We introduce and study dynamical systems and measures on stationary generalized Bratteli diagrams $B$ that are represented as the union of countably many classical Pascal-Bratteli diagrams. We describe all ergodic tail invariant measures on…

For every non-elementary hyperbolic group, we introduce the Manhattan curve associated to any pair of left-invariant hyperbolic metrics which are quasi-isometric to a word metric. It is convex; we show that it is continuously differentiable…

We study infinite graph-directed iterated function systems (GIFS) whose underlying graph is not strongly connected and has countably many vertices and edges. In addition to a summability condition for the physical potential, we provide…

Let $(X,G)$ be a topological dynamical system, given by the action of a is a countable discrete infinite group on a compact metric space $X$. We prove that if $(X,G)$ is minimal, then it is either diam-mean $m$-equicontinuious or diam-mean…

A critically finite branched self-cover $f: (S^2, P) \to (S^2, P)$ determines naturally three iterated function systems: one on the pure mapping class group of the sphere marked at $P$, one on the Teichm\"uller space of the sphere marked at…

This paper establishes $C^m$ topological equivalence of nonautonomous semilinear difference equation with its linearization and generalizes the obtained results to discrete random dynamical systems, considering both, global and local,…

We introduce a comprehensive framework for subordinacy theory applicable to long-range operators on $\ell^2(\mathbb Z)$, bridging dynamical systems and spectral analysis. For finite-range operators, we establish a correspondence between the…

Following the approach pioneered by Eckhaus, Mielke, Schneider, and others for reaction diffusion systems [E, M1, M2, S1, S2, SZJV], we systematically derive formally by multiscale expansion and justify rigorously by Lyapunov-Schmidt…

Model studies indicate that many climate subsystems, especially ecosystems, may be vulnerable to 'tipping': a 'catastrophic process' in which a system, driven by gradually changing external factors, abruptly transitions (or 'collapses')…

We investigate the large scale chaotic, topological structure of the trajectories of an infinite sequence of dispersing, hence ergodic, $2D$ billiards with the configuration space $Q_n=\mathbb{T}^2 \setminus \bigcup_{i=0}^{n-1} D_i$, where…

We show that the dynamical system associated by Putnam to a pair of graph embeddings is identical to the shift map on the limit space of a self-similar groupoid action on a graph. Moreover, performing a certain out-split on said graph gives…

It has been more than twenty years since Moshe Newman, based on work by Neil Calkin and Herbert Wilf, introduced an explicit bijection between the rational and natural numbers. Interestingly, this bijection is dynamic in nature. Indeed,…

Prediction via deterministic continuous-time models will always be subject to model error, for example due to unexplainable phenomena, uncertainties in any data driving the model, or discretisation/resolution issues. In this paper, we build…

Expansivity, Li-Yorke chaos and shadowing are popular and well-studied notions of dynamical systems. Several simple and useful characterizations of these notions within the setting of linear dynamics were obtained recently. We explore these…