Some open problems in dynamical systems.
Herman, Michael (1998)
Documenta Mathematica
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Herman, Michael (1998)
Documenta Mathematica
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Rocco Duvenhage (2012)
Studia Mathematica
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Relatively independent joinings of W*-dynamical systems are constructed. This is intimately related to subsystems of W*-dynamical systems, and therefore we also study general properties of subsystems, in particular fixed point subsystems and compact subsystems. This allows us to obtain characterizations of weak mixing and relative ergodicity, as well as of certain compact subsystems, in terms of joinings.
A. N. Sharkovskii (1989)
Banach Center Publications
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Ou, Baiyu, Liu, Desheng (2010)
Discrete Dynamics in Nature and Society
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Miguel A. F. Sanjuán (1992)
Acta Universitatis Carolinae. Mathematica et Physica
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Anishchenko, Vadim S., Strelkova, Galina I. (1998)
Discrete Dynamics in Nature and Society
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Basilio Messano, Antonio Zitarosa (1989)
Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti
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We introduce generalized dynamical systems (including both dynamical systems and discrete dynamical systems) and give the notion of minimal set of a generalized dynamical system. Then we prove a generalization of the classical G.D. Birkhoff theorem about minimal sets of a dynamical system and some propositions about generalized discrete dynamical systems.
Awadalla, Attia.A. (2006)
APPS. Applied Sciences
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N. N. Chentsova (1989)
Banach Center Publications
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Ou, Baiyu, Liu, Desheng (2010)
Mathematical Problems in Engineering
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Basilio Messano, Antonio Zitarosa (1989)
Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni
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We introduce generalized dynamical systems (including both dynamical systems and discrete dynamical systems) and give the notion of minimal set of a generalized dynamical system. Then we prove a generalization of the classical G.D. Birkhoff theorem about minimal sets of a dynamical system and some propositions about generalized discrete dynamical systems.
Lluís Alsedà, Sara Costa (2009)
Fundamenta Mathematicae
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The aim of this paper is twofold. On the one hand, we want to discuss some methodological issues related to the notion of strange nonchaotic attractor. On the other hand, we want to formulate a precise definition of this kind of attractor, which is "observable" in the physical sense and, in the two-dimensional setting, includes the well known models proposed by Grebogi et al. and by Keller, and a wide range of other examples proposed in the literature. Furthermore, we analytically prove...
Andrzej Pelczar (1989)
Banach Center Publications
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Vadivasova, T.E., Sosnovtseva, O.V., Balanov, A.G., Astakhov, V.V. (2000)
Discrete Dynamics in Nature and Society
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Stefanski, Andrzej, Kapitaniak, Tomasz (2000)
Discrete Dynamics in Nature and Society
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David Cheban (2014)
Nonautonomous Dynamical Systems
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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...
Anna Cima, Armengol Gasull, Francesc Mañosas (2001)
Annales Polonici Mathematici
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In LaSalle's book "The Stability of Dynamical Systems", the author gives four conditions which imply that the origin of a discrete dynamical system defined on ℝ is a global attractor, and proposes to study the natural extensions of these conditions in ℝⁿ. Although some partial results are obtained in previous papers, as far as we know, the problem is not completely settled. In this work we first study the four conditions and prove that just one of them implies that the origin is a global...