Related papers: $p$-adic dynamical systems of the function $a x^{-…

This study evaluates data-driven models from a dynamical system perspective, such as unstable fixed points, periodic orbits, chaotic saddle, Lyapunov exponents, manifold structures, and statistical values. We find that these dynamical…

In this paper, we study dynamical properties as shadowing and structural stability for a class of dynamics on $\mathbb{Z}_p$ and $\mathbb{Q}_p$, where $p \geq 2$ is a prime number. In particular, we prove that if $f: \mathbb{Z}_p \to…

We continue previous work to count non-equivalent dynamical systems over finite fields generated by polynomials or rational functions.

Inspired by the techniques of Givental and Th\'eret, we provide a proof with generating functions of a recent result of Ginzburg-G\"urel concerning the periodic points of Hamiltonian diffeomorphisms of $\mathbb{C}\text{P}^d$. For instance,…

This paper concerns two-dimensional Filippov systems --- ordinary differential equations that are discontinuous on one-dimensional switching manifolds. In the situation that a stable focus transitions to an unstable focus by colliding with…

We present sufficient conditions for the existence of a periodic solution for a class of systems describing the periodically forced motion of a massive point on a compact surface with a boundary.

We study the dynamics of four families of methods obtained with a weight function from a convex combination of Newton's method and a Newton-Halley type method on polynomials with two roots. We find the analytical expressions for the fixed…

Dynamical systems with quadratic or polynomial drift exhibit complex dynamics, yet compared to nonlinear systems in general form, are often easier to analyze, simulate, control, and learn. Results going back over a century have shown that…

We compute the motivic nearby cycles of functions obtained by composition of two functions with distinct sets of variables with a two variable function

We review some of the recent developments and prove new results concerning frames and Bessel systems generated by iterations of the form $\{A^ng: g\in G,\, n=0,1,2,\dots \}$, where $A$ is a bounded linear operators on a separable complex…

We consider two minimal models of active fluid droplets that exhibit complex dynamics including steady motion, deformation, rotation and oscillating motion. First we consider a droplet with a concentration of active contractile matter…

This note aims to bring attention to a simple class of discrete dynamical systems exhibiting some complex behaviour. Each of these systems is defined as a self-mapping of the unit square and is obtained by coupling two families of…

In this manuscript we consider the stability of periodic solutions to Lambda-Omega lattice dynamical systems. In particular, we show that an appropriate ansatz casts the lattice dynamical system as an infinite-dimensional fast-slow…

In this paper we introduce and study the notion of dynamical forcing. Basically, we develop a toolkit of techniques to produce finitely presented groups which can only act on the circle with certain prescribed dynamical properties. As an…

The power system, a fundamental public utility, is increasingly important due to growing global electricity demand. Recent large-scale blackouts (e.g., Iberian Peninsula, UK) have raised concerns about transient stability under impact…

In this work we introduce a topological method for the search of fixed points and periodic points for continuous maps defined on generalized rectangles in finite dimensional Euclidean spaces. We name our technique "Stretching Along the…

In local relative $p$-adic Hodge theory, we show that the Galois cohomology of a finite height crystalline representation (up to a twist) is essentially computed via the (Fontaine--Messing) syntomic complex with coefficients in the…

We consider a specific dynamical system of groups formation. It is based simultaneously on a gradient competition between groups and a strong accumulation inside groups. Such a dynamical system demonstrates interesting behavior of densities…

In this document, we deal with the stabilization problem of slow-fast systems (or singularly perturbed Ordinary Differential Equations) at a non-hyperbolic point. The class of systems studied here have the following properties: 1) they have…

We use symplectic tools to establish a smooth variant of Franks theorem for a closed orientable surface of positive genus $g$; it implies that a symplectic diffeomorphism isotopic to the identity with more than $2g-2$ fixed points, counted…