动力系统

This paper introduces a novel computer-assisted method for detecting and constructively proving the existence of cusp bifurcations in differential equations. The approach begins with a two-parameter continuation along which a tool based on…

We extend the concept of a Hubbard tree, well established and useful in the theory of polynomial dynamics, to the dynamics of transcendental entire functions. We show that Hubbard trees in the strict traditional sense, as invariant compact…

This paper introduces a novel safety-critical control method through the synthesis of control barrier functions (CBFs) for systems with high-relative-degree safety constraints. By extending the procedure of CBF backstepping, we propose…

We study the relaxation dynamics of the inertial Kuramoto model toward a phase-locked state from a generic initial phase configuration. For this, we propose a sufficient framework in terms of initial data and system parameters for…

Delay embedding methods are a staple tool in the field of time series analysis and prediction. However, the selection of embedding parameters can have a big impact on the resulting analysis. This has led to the creation of a large number of…

Dynamical networks are versatile models that can describe a variety of behaviours such as synchronisation and feedback. However, applying these models in real world contexts is difficult as prior information pertaining to the connectivity…

We survey recent developments in fractal analysis of regular and slow-fast dynamical systems using Minkowski dimension. Our focus is on spiral trajectories near monodromic limit periodic sets in regular systems and entry-exit sequences in…

Online deception and financial scams represent a pervasive threat in the digital age, yet a quantitative analysis and understanding of their propagation is lacking. This study introduces a novel model based on the framework of…

In this paper, we study the distribution of renormalized gaps between slopes of saddle connections on translation surfaces. Specifically, we describe a procedure for finding the "winning holonomy vectors" as defined by…

In this paper, we first show that the collection of all subsets of \( \mathbb{R} \) having lower dimension \( \gamma \in [0,1] \) is dense in \( \Pi(\mathbb{R}) \), the space of compact subsets of \( \mathbb{R} \). Furthermore, we show that…

We investigate the zero-temperature large deviation principle for equilibrium states in the context of distance-expanding maps. The logarithmic-type zero-temperature limit in the large deviation principle induces a tropical algebra…

We establish abstract local limit theorems for hitting times and return-times of suitable sequences (A_{l}) of asymptotically rare events in ergodic probability preserving dynamical systems, including versions for tuples of consecutive…

Equilibrium states are natural dynamical analogues of Gibbs states in thermodynamic formalism. This paper investigates their computability within the framework of Computable Analysis. We show that the unique equilibrium state for a…

Coarse expanding conformal systems were introduced by P. Ha\"issinsky and K. M. Pilgrim to study the essential dynamical properties of certain rational maps on the Riemann sphere in complex dynamics from the point of view of Sullivan's…

Expanding Thurston maps form a class of branched covering maps on the topological $2$-sphere $S^{2}$, which are topological models of some non-uniformly expanding rational maps without any smoothness or holomorphicity assumption initially…

Simultaneous deterministic and weakly stochastic dynamics of multiple populations described by a large system of ODE's is considered in the phase space of population sizes and ODE's parameters. We show that many practically interesting…

We construct a general class of correspondences on hyperelliptic Riemann surfaces of arbitrary genus that combine finitely many Fuchsian genus zero orbifold groups and Blaschke products. As an intermediate step, we first construct analytic…

We identify two nontrivial errors in the proof of the main results of the work \emph{generalized baby Mandelbrot sets adorned with halos in families of rational maps} by Jang, So, and Marotta. We correct these errors, showing that the main…

Have you ever played or watched a game of pool? If so, you have already seen a billiard system in action. In mathematics and physics, a billiard system describes a ball that moves in straight lines and bounces off walls. Despite these…

An Anosov flow on a smooth three-manifold $M$ gives rise to a Liouville structure on $\mathbb{R} \times M$ by a construction of Mitsumatsu. In a recent paper, Cieliebak, Lazarev, Massoni and Moreno ask whether an embedded torus $\Sigma…