Asymptotic stability of dynamical systems with multiplicative perturbations
Katarzyna Horbacz (1989)
Annales Polonici Mathematici
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Katarzyna Horbacz (1989)
Annales Polonici Mathematici
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Henryk Gacki
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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...
Dawid Czapla (2012)
Annales Polonici Mathematici
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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...
Tomasz Szarek (1997)
Annales Polonici Mathematici
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We prove a new sufficient condition for the asymptotic stability of Markov operators acting on measures. This criterion is applied to iterated function systems.
Didier Pilod (2014-2015)
Séminaire Laurent Schwartz — EDP et applications
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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.
M. Ślęczka (2004)
Annales Polonici Mathematici
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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.
Karol Baron, Andrzej Lasota (1998)
Annales Polonici Mathematici
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We consider the family 𝓜 of measures with values in a reflexive Banach space. In 𝓜 we introduce the notion of a Markov operator and using an extension of the Fortet-Mourier norm we show some criteria of the asymptotic stability. Asymptotically stable Markov operators can be used to construct coloured fractals.
Li, Weiye, Szidarovszky, Ferenc (1999)
Southwest Journal of Pure and Applied Mathematics [electronic only]
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Katarzyna Pichór (1998)
Annales Polonici Mathematici
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We study the asymptotic behaviour of the Markov semigroup generated by an integro-partial differential equation. We give new sufficient conditions for asymptotic stability of this semigroup.
B. Vrdoljak (1980)
Matematički Vesnik
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Katarzyna Horbacz (1998)
Annales Polonici Mathematici
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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.
Zahreddine, Ziad (2001)
Bulletin of the Malaysian Mathematical Sciences Society. Second Series
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Mimia Benhadri, Tomás Caraballo (2022)
Mathematica Bohemica
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This paper addresses the stability study for nonlinear neutral differential equations. Thanks to a new technique based on the fixed point theory, we find some new sufficient conditions ensuring the global asymptotic stability of the solution. In this work we extend and improve some related results presented in recent works of literature. Two examples are exhibited to show the effectiveness and advantage of the results proved.
J. Terjéki (1979)
Annales Polonici Mathematici
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Joanna Kubieniec (2016)
Annales Mathematicae Silesianae
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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.
Vrkoč, I.
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