动力系统
In [J. Cantarella, J. Parsley, J. Geom. Phys. 60:1127 (2010)] Cantarella and Parsley introduced the notion of submanifold helicity. In the present paper we investigate properties of surface helicity and in particular answer two open…
A minimal equicontinuous action of a group $G$ on a Stone space $X$ is called a subodometer. If such a subodometer arises from a group rotation, we refer to it as an odometer. For subodometers $(X,G)$ we show that the hyperspace…
We investigate instability phenomena for linear evolution equations within the framework of $C_0$--semigroups on infinite--dimensional spaces. We show that Devaney chaos, being formulated in purely topological terms, may depend on the…
For generalized Frenkel-Kontorova models subjected to almost-periodic media, employing both the KAM method and the approach of `anti-integrable' limits, two different types of equilibria are obtained in…
Given two one-dimensional families $f$ and $g$ of regular plane polynomial automorphisms parameterised by an algebraic curve $B$, all defined over some number field $K$, such that one of them is dissipative, we prove that at any parameter…
Universal approximation theorems establish the expressive capacity of neural network architectures. For dynamical systems, existing results are limited to finite time horizons or systems with a globally stable equilibrium, leaving…
We study feedback control of twisted states in the Kuramoto model (KM) of identical oscillators defined on deterministic nearest neighbor graphs containing complete simple ones when it may have phase-lag. Bifurcations of such twisted…
This paper investigates the motion of a rotating test body in the Schwarzschild space-time. After reduction, this problem reduces to an analysis of a three-degree-of-freedom. Hamiltonian system whose desired trajectories lie on the…
The degeneracy of central configurations in the planar $N$-body problem makes their enumeration problem hard and the related dynamics appealing. To truly understand the bifurcations of central configurations, we should work in the FULL…
In this paper we study the phase portraits and bifurcation diagram of the symmetric singularities of codimensions zero, one and two of planar reversible vector fields having a line of reversibility.
The Sierpinski tetrahedron has a remarkable property: It is projected to squares in three orthogonal directions, and moreover, to sets with positive Lebesgue measures in numerous directions. This paper proposes a method for characterizing…
We show that any uniformly escaping and wandering dynamics of a holomorphic function on a compact subset of the plane can be realised by a transcendental meromorphic function on $\mathbb{C}$. More precisely, let $\varphi$ be a holomorphic…
We introduce a Toeplitz-based framework for data-driven spectral estimation of linear evolution operators in dynamical systems. Focusing on transfer and Koopman operators from equilibrium trajectories without access to the underlying…
In this paper, we characterize all polynomial Kolmogorov vector fields for which the standard $n$-sphere is invariant. We exhibit completely integrable Kolmogorov vector fields of degree $m$ on $\mathbb{S}^n$ for any $m >2$. Then, we show…
This study investigates how the interaction between gene expression time delay and domain size governs spatio-temporal pattern formation in a reaction-diffusion system. To investigate these phenomena, we utilize a modified version of the…
We investigate finite-time Lyapunov exponents (FTLEs), a measure for exponential separation of input perturbations, of deep neural networks within the framework of continuous-depth neural ODEs. We demonstrate that FTLEs are powerful…
We prove a logarithm law-type result for the spiraling of geodesics around certain types of compact subsets (e.g. quotients of periodic Morse flats) in quotients of rank one CAT(0) spaces.
It is known that $C^1$-smooth strictly convex Radon norms in $\mathbb{R}^2$ can be characterized by the property that the outer billiard map, which corresponds to the unit ball of the norm, has an invariant curve consisting of 4-periodic…
In this paper, we introduce a new technique to study the distribution in residue classes of sets of integers with digit and sum-of-digits restrictions. From our main theorem, we derive a necessary and sufficient condition for integers with…
For each integer $d\geq 2$, let $M_d$ denote the moduli space of maps $f: \mathbb{P}^1\to \mathbb{P}^1$ of degree $d$. We study the geometric configurations of subsets of postcritically finite (or PCF) maps in $M_d$. A complex-algebraic…