Related papers: Flexible periodic points
Let $(X,f_{1,\infty})$ be a nonautonomous dynamical system. In this paper we summarize known definitions of periodic points for general nonautonomous dynamical systems and propose a new, very natural, definition of asymptotic periodicity.…
Stability is a key property of dynamical systems. In some cases, we want to change unstable system into stable one to achieve certain goals in engineering. Here, we present an example of a $3$ dimensional switched system that alternates…
For the system of an inverted spherical pendulum with friction and a periodically moving pivot point we prove the existence of at least one periodic solution with the additional property of being falling-free. The last means that the…
We study relations between transitivity, mixing and periodic points on dendrites. We prove that when there is a point with dense orbit which is not an endpoint, then periodic points are dense and there is a terminal periodic decomposition…
This paper concerns piecewise-smooth maps on $\mathbb{R}^d$ that are continuous but not differentiable on switching manifolds (where the functional form of the map changes). The stability of fixed points on switching manifolds is…
We consider certain one dimensional ordinary stochastic differential equations driven by additive Brownian motion of variance $\varepsilon ^2$. When $\varepsilon =0$ such equations have an unstable non-hyperbolic fixed point and the drift…
The existence, uniqueness, and asymptotic stability of modulo periodic Poisson stable solutions of dynamic equations on a periodic time scale are investigated. The model under investigation involves a term which is constructed via a Poisson…
We construct a smooth nontrivial mixed partially hyperbolic system and explicitly identify its skeleton. This example shares characteristics with the classical examples. Moreover, the support of each physical measure contains three fixed…
We study the stable behaviour of discrete dynamical systems where the map is convex and monotone with respect to the standard positive cone. The notion of tangential stability for fixed points and periodic points is introduced, which is…
We consider generic differential equations in $\mathbb{R}$ with a finite number of hyperbolic equilibria, which are subject to $\omega$--periodic instantaneous perturbative pulses ($\omega>0$). Using the time-$ \omega$ map of the original…
Consider the dynamical system constitued by a continuous function $F:\mathcal{A}^\mathbb{N}\to\mathcal{A}^\mathbb{N}$ where $\mathcal{A}$ is a finite alphabet. The perturbed counterpart, denoted by $F_\epsilon$, is obtained after each…
The variation of the velocity of a periodic signal and its frequency along the world line of a standard emitter (at rest with an observer) are considered in a space with affine connections and metrics. It is shown that the frequency of the…
We provide a constructive method designed in order to control the stability of a given periodic orbit of a general completely integrable system. The method consists of a specific type of perturbation, such that the resulting perturbed…
We prove results related to robust transitivity and density of periodic points of Partially Hyperbolic Diffeomorphisms under conditions involving Accessibility and a property in the tangent bundle .
A sofic group $G$ is said to be flexibly stable if every sofic approximation to $G$ can converted to a sequence of disjoint unions of Schreier graphs by modifying an asymptotically vanishing proportion of edges. We establish that if…
A thin and narrow rectangular plate having the two short edges hinged and the two long edges free is considered. A nonlinear nonlocal evolution equation describing the deformation of the plate is introduced: well-posedness and existence of…
By varying a parameter of a one-dimensional piecewise smooth map, stable periodic orbits are observed. In this paper, complete analytic characterization of these stable periodic orbits is obtained. An interesting relationship between the…
The motion of a spinning football brings forth the possible existence of a whole class of finite dynamical systems where there may be non-denumerably infinite number of fixed points. They defy the very traditional meaning of the fixed point…
It is known that volume hyperbolicity (partial hyperbolicity and uniform expansion or contraction of the volume in the extremal bundles) is a necessary condition for robust transitivity or robust chain recurrence hence for tameness. In this…
Summary: A system of autonomous ordinary differential equations depending on a small parameter is considered such that the unperturbed system has an invariant manifold of periodic solutions that is not normally hyperbolic but is normally…