Browsing by Subject "dynamical system"

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Dynamika i chaos dla odwzorowań odcinka i grafu
(Data obrony: 2018-10-25) Bączek, Jan
Wydział Matematyki Stosowanej
Access status: Open Access ,
Is a fractional system a dynamical system?
(Wydawnictwa AGH, 2011) Mitkowski, Wojciech
In recent years we may notice a return to the analysis of fractional systems. Such systems are described in the form of differential equations with fractional derivative. In this paper we notice the fact that this type of differential equations does not generate dynamical system. We show suitable numerical example.
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Modele biologiczne typu drapieżnik-ofiara
(Data obrony: 2011-11-10) Brożyna, Przemysław
Wydział Matematyki Stosowanej
Access status: Open Access ,
On potential kernels associated with random dynamical systems
(2015) Hmissi, Mohamed; Mokchaha-Hmissi, Farida Chedly; Hmissi, Aya
Let $(\theta,\varphi)$ be a continuous random dynamical system defined on a probability space $(\Omega,\mathcal{F},\mathbb{P})$ and taking values on a locally compact Hausdorff space $E$. The associated potential kernel $V$ is given by $Vf(\omega ,x)= \int\limits_{0}^{\infty} f(\theta_{t}\omega,\varphi(t,\omega)x)dt, \quad \omega \in \Omega, x\in E.$ In this paper, we prove the equivalence of the following statements: 1. The potential kernel of $(\theta,\varphi)$ is proper, i.e. $Vf$ is $x$-continuous for each bounded, $x$-continuous function $f$ with uniformly random compact support. 2. $(\theta,\varphi)$ has a global Lyapunov function, i.e. a function $L:\Omega\times E \rightarrow (0,\infty)$ which is $x$-continuous and $L(\theta_t\omega, \varphi(t,\omega)x)\downarrow 0$ as $t\uparrow \infty$. In particular, we provide a constructive method for global Lyapunov functions for gradient-like random dynamical systems.
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Synchroniczne powracanie i niezależność orbit
(Data obrony: 2016-05-12) Seń, Adrian
Wydział Matematyki Stosowanej
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Własności ergodyczne układów dynamicznych na gładkim wypukło-wklęsłym bilardzie
(Data obrony: 2010-01-12) Feldman, Jacek Grzegorz
Wydział Matematyki Stosowanej