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Analytic enclosure of the fundamental matrix solution

Roberto Castelli, Jean-Philippe Lessard, Jason D. Mireles James (2015)

Applications of Mathematics

This work describes a method to rigorously compute the real Floquet normal form decomposition of the fundamental matrix solution of a system of linear ODEs having periodic coefficients. The Floquet normal form is validated in the space of analytic functions. The technique combines analytical estimates and rigorous numerical computations and no rigorous integration is needed. An application to the theory of dynamical system is presented, together with a comparison with the results obtained by computing...

Compact Global Chaotic Attractors of Discrete Control Systems

David Cheban (2014)

Nonautonomous Dynamical Systems

The paper is dedicated to the study of the problem of existence of compact global chaotic attractors of discrete control systems and to the description of its structure. We consider so called switched systems with discrete time xn+1 = fν(n)(xn), where ν : ℤ+ ⃗ {1,2,...,m}. If m ≥ 2 we give sufficient conditions (the family M := {f1,f2,...,fm} of functions is contracting in the extended sense) for the existence of a compact global chaotic attractor. We study this problem in the framework of non-autonomous...

Group actions on monotone skew-product semiflows with applications

Feng Cao, Mats Gyllenberg, Yi Wang (2016)

Journal of the European Mathematical Society

We discuss a general framework of monotone skew-product semiflows under a connected group action. In a prior work, a compact connected group G -action has been considered on a strongly monotone skew-product semiflow. Here we relax the strong monotonicity and compactness requirements, and establish a theory concerning symmetry or monotonicity properties of uniformly stable 1-cover minimal sets. We then apply this theory to show rotational symmetry of certain stable entire solutions for a class of...

Metric Entropy of Nonautonomous Dynamical Systems

Christoph Kawan (2014)

Nonautonomous Dynamical Systems

We introduce the notion of metric entropy for a nonautonomous dynamical system given by a sequence (Xn, μn) of probability spaces and a sequence of measurable maps fn : Xn → Xn+1 with fnμn = μn+1. This notion generalizes the classical concept of metric entropy established by Kolmogorov and Sinai, and is related via a variational inequality to the topological entropy of nonautonomous systems as defined by Kolyada, Misiurewicz, and Snoha. Moreover, it shares several properties with the classical notion...

Pullback incremental attraction

Peter E. Kloeden, Thomas Lorenz (2014)

Nonautonomous Dynamical Systems

A pullback incremental attraction, a nonautonomous version of incremental stability, is introduced for nonautonomous systems that may have unbounded limiting solutions. Its characterisation by a Lyapunov function is indicated.

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