Displaying similar documents to “Asymptotic stability of dynamical systems with multiplicative perturbations”

Asymptotic stability of a linear Boltzmann-type equation

Roksana Brodnicka, Henryk Gacki (2014)

Applicationes Mathematicae

Similarity:

We present a new necessary and sufficient condition for the asymptotic stability of Markov operators acting on the space of signed measures. The proof is based on some special properties of the total variation norm. Our method allows us to consider the Tjon-Wu equation in a linear form. More precisely a new proof of the asymptotic stability of a stationary solution of the Tjon-Wu equation is given.

Asymptotic Stability of Zakharov-Kuznetsov solitons

Didier Pilod (2014-2015)

Séminaire Laurent Schwartz — EDP et applications

Similarity:

In this report, we review the proof of the asymptotic stability of the Zakharov-Kuznetsov solitons in dimension two. Those results were recently obtained in a joint work with Raphaël Côte, Claudio Muñoz and Gideon Simpson.

Randomly connected dynamical systems - asymptotic stability

Katarzyna Horbacz (1998)

Annales Polonici Mathematici

Similarity:

We give sufficient conditions for asymptotic stability of a Markov operator governing the evolution of measures due to the action of randomly chosen dynamical systems. We show that the existence of an invariant measure for the transition operator implies the existence of an invariant measure for the semigroup generated by the system.

Random Dynamical Systems with Jumps and with a Function Type Intensity

Joanna Kubieniec (2016)

Annales Mathematicae Silesianae

Similarity:

In paper [4] there are considered random dynamical systems with randomly chosen jumps acting on Polish spaces. The intensity of this process is a constant λ. In this paper we formulate criteria for the existence of an invariant measure and asymptotic stability for these systems in the case when λ is not constant but a Lipschitz function.

A criterion of asymptotic stability for Markov-Feller e-chains on Polish spaces

Dawid Czapla (2012)

Annales Polonici Mathematici

Similarity:

Stettner [Bull. Polish Acad. Sci. Math. 42 (1994)] considered the asymptotic stability of Markov-Feller chains, provided the sequence of transition probabilities of the chain converges to an invariant probability measure in the weak sense and converges uniformly with respect to the initial state variable on compact sets. We extend those results to the setting of Polish spaces and relax the original assumptions. Finally, we present a class of Markov-Feller chains with a linear state space...

Asymptotic stability in L¹ of a transport equation

M. Ślęczka (2004)

Annales Polonici Mathematici

Similarity:

We study the asymptotic behaviour of solutions of a transport equation. We give some sufficient conditions for the complete mixing property of the Markov semigroup generated by this equation.

Applications of the Kantorovich-Rubinstein maximum principle in the theory of Markov semigroups

Henryk Gacki

Similarity:

We present new sufficient conditions for the asymptotic stability of Markov operators acting on the space of signed measures. Our results are based on two principles. The first one is the LaSalle invariance principle used in the theory of dynamical systems. The second is related to the Kantorovich-Rubinstein theorems concerning the properties of probability metrics. These criteria are applied to stochastically perturbed dynamical systems, a Poisson driven stochastic differential equation...