A Billingsley type theorem for Bowen topological entropy of nonautonomous dynamical systems
Open Mathematics, 2022 Abstract This article is devoted to the study of the Bowen topological entropy for nonautonomous dynamical systems, which is an extension of the classical definition of Bowen topological entropy. We show that the Bowen topological entropy can be determined by the local entropies of measures for nonautonomous dynamical systems, which ...
Zhang Bin, Liu Lei
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Topological entropy of nonautonomous dynamical systems [PDF]
Journal of Differential Equations, 2020 Let $\mathcal{M}(X)$ be the space of Borel probability measures on a compact metric space $X$ endowed with the weak$^\ast$-topology. In this paper, we prove that if the topological entropy of a nonautonomous dynamical system $(X,\{f_n\}_{n=1}^{+\infty})$ vanishes, then so does that of its induced system $(\mathcal{M}(X),\{f_n\}_{n=1}^{+\infty ...
Liu, Kairan, Qiao, Yixiao, Xu, Leiye
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Method of Limiting Differential Inclusions and Asymptotic Behavior of Systems with Relay Controls
Известия Иркутского государственного университета: Серия "Математика", 2022 In this paper, problems of asymptotic behavior of non-autonomous controlled systems with a matrix of derivatives and the feedbacks of relay type are considered.
I. A. Finogenko
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Weak topologies for Carathéodory differential equations: continuous dependence, exponential dichotomy and attractors [PDF]
, 2019 Producción CientíficaWe introduce new weak topologies and spaces of Carathéodory functions where the solutions of the ordinary differential equations depend continuously on the initial data and vector fields. The induced local skew-product flow is proved
Longo, Iacopo Paolo +2 more
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Topological entropy of nonautonomous piecewise monotone dynamical systems on the interval [PDF]
Fundamenta Mathematicae, 1999 A nonautonomous discrete dynamical system given by a sequence of compact metric spaces \((X_{i})_{i=1}^{\infty}\) and a sequence of continuous maps \((f_{i})_{i=1}^{\infty}\), \(f_{i}: X_{i}\to X_{i+1}\) is considered. In the previous paper [Random Comput. Dyn.
Kolyada, Sergii +2 more
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On attractors, spectra and bifurcations of random dynamical systems [PDF]
, 2015 In this thesis a number of related topics in random dynamical systems theory are studied: local attractors and attractor-repeller pairs, the exponential dichotomy spectrum and bifurcation theory.
Callaway, Mark
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Entropy increase in switching systems [PDF]
, 2013 The relation between the complexity of a time-switched dynamics and the complexity of its control sequence depends critically on the concept of a non-autonomous pullback attractor.
Amigó +9 more
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Topological entropy of nonautonomous dynamical systems on uniform spaces
Journal of Differential Equations, 2023 In this paper, we focus on some properties, calculations and estimations of topological entropy for a nonautonomous dynamical system $(X,f_{0,\infty})$ generated by a sequence of continuous self-maps $f_{0,\infty}=\{f_n\}_{n=0}^{\infty}$ on a compact uniform space $X$. We obtain the relations of topological entropy among $(X, f_{0,\infty})$, its $k$-th
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Rigorous numerics for PDEs with indefinite tail: existence of a periodic solution of the Boussinesq equation with time-dependent forcing [PDF]
, 2015 We consider the Boussinesq PDE perturbed by a time-dependent forcing. Even though there is no smoothing effect for arbitrary smooth initial data, we are able to apply the method of self-consistent bounds to deduce the existence of smooth classical ...
Czechowski, Aleksander +1 more
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Non-Atkinson perturbations of nonautonomous linear Hamiltonian systems: exponential dichotomy and nonoscillation [PDF]
, 2017 Producción CientíficaWe analyze the presence of exponential dichotomy (ED) and of global existence of Weyl functions $M^\pm$ for one-parametric families of finite-dimensional nonautonomous linear Hamiltonian systems defined along the orbits of a compact ...
Núñez Jiménez, María del Carmen +1 more
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