Related papers: Generic chaos on dendrites
Many dynamical systems of different complexity, e.g. 1D logistic map, the Lorentz equations, or real phenomena, like turbulent convection, show chaotic behaviour. Despite huge differences, the dynamical scenarios for these systems are…
We prove the presence of topological chaos at high internal energies for a new class of mechanical refraction billiards coming from Celestial Mechanics. Given a smooth closed domain $D\in\mathbb{R}^2$, a central mass generates a Keplerian…
We investigate the relation between the chaotic dynamics and the hierarchical phase-space structure of generic Hamiltonian systems. We demonstrate that even in ideal situations when the phase space is dominated by an exactly self-similar…
Let $T$ be a continuous self-map of a compact metric space $X$. The transformation $T$ induces natural a continuous self-map $T_K$ on the hyperspace $K(X)$ of all non-empty closed subsets of $X$. In this paper, we show that the system…
We study Li-Yorke chaos for sequences of continuous linear operators from an \(F\)-space to a normed space. We introduce the \emph{D-phenomenon} to establish a common dense lineable criterion that encompasses properties such as recurrence,…
Chaos is a fundamental phenomenon in nonlinear dynamics, manifesting as irregular and unpredictable behavior across various physical systems. Among the diverse routes to chaos, intermittent chaos is a distinct transition pathway,…
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…
Dynamical Systems theory generally deals with fixed point iterations of continuous functions. Computation by Turing machine although is a fixed point iteration but is not continuous. This specific category of fixed point iterations can only…
Let $X$ be a dendrite with set of endpoints $E(X)$ closed and let $f:~X \to X$ be a continuous map with zero topological entropy. Let $P(f)$ be the set of periodic points of $f$. We prove that if $L$ is an infinite $\omega$-limit set of $f$…
The aim of the paper is to correct and improve some results concerning distributional chaos of type 3. We show that in a general compact metric space, distributional chaos of type 3, denoted DC3, even when assuming the existence of an…
We show that deterministic systems with strong nonlinearities seem to be more appropriate to model sandpiles than stochastic systems or deterministic systems in which discontinuities are the only nonlinearity. In particular, we are able to…
In a generic dynamical system chaos and regular motion coexist side by side, in different parts of the phase space. The border between these, where trajectories are neither unstable nor stable but of marginal stability, manifests itself…
We present numerical simulation results of driven vortex lattices in presence of random disorder at zero temperature. We show that the plastic dynamics is readily understood in the framework of chaos theory. Intermittency "routes to chaos"…
In finite-dimensional, chaotic, Lorenz-like wave-particle dynamical systems one can find diffusive trajectories, which share their appearance with that of laminar chaotic diffusion [Phys. Rev. Lett. 128, 074101 (2022)] known from delay…
The steady state for a system of N particle under the influence of an external field and a Gaussian thermostat and colliding with random "virtual" scatterers can be obtained explicitly in the limit of small field. We show the sequence of…
Transitions to chaos in archetypal low-dimensional nonlinear maps offer real and precise model systems in which to assess proposed generalizations of statistical mechanics. The known association of chaotic dynamics with the structure of…
The concept of A-coupled-expanding map, which is one of the more natural and useful ideas generalized the horseshoe map, is well known as a criterion of chaos. It is well known that distributional chaos is one of the concepts which reflect…
We show that every dendrite satisfying the condition that no subtree of it contains all free arcs admits a transitive, even exactly Devaney chaotic map with arbitrarily small entropy. This gives a partial answer to a question of Baldwin…
Coexistence of various ordered chaotic states in a Hamiltonian system is studied with the use of a symplectic coupled map lattice. Besides the clustered states for the attractive interaction, a novel chaotic ordered state is found for a…
The statistics of gaps between quantum energy levels is a hallmark criterion in quantum chaos and quantum integrability studies. The relevant distributions corresponding to exactly integrable vs. fully chaotic systems are universal and…