Some open problems in dynamical systems.
Herman, Michael (1998)
Documenta Mathematica
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Herman, Michael (1998)
Documenta Mathematica
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Coke S. Reed (1973)
Colloquium Mathematicae
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Emmanuel Lesigne, Anthony Quas, Máté Wierdl (2003)
Bulletin de la Société Mathématique de France
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The symbolic dynamical system associated with the Morse sequence is strictly ergodic. We describe some topological and metrical properties of the Cartesian powers of this system, and some of its other self-joinings. Among other things, we show that non generic points appear in the fourth power of the system, but not in lower powers. We exhibit various examples and counterexamples related to the property of weak disjointness of measure preserving dynamical systems.
Thierry de la Rue (2004)
Colloquium Mathematicae
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We give an example of a dynamical system which is mixing relative to one of its factors, but for which relative mixing of order three does not hold.
Oleg Zubelevich (2015)
Applicationes Mathematicae
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We give an existence theorem for bounded solutions to a system of second order ODEs. Dynamical applications are considered.
Alexandre I. Danilenko (2010)
Studia Mathematica
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It is shown that each subset of positive integers that contains 2 is realizable as the set of essential values of the multiplicity function for the Koopman operator of some weakly mixing transformation.
Rocco Duvenhage (2009)
Studia Mathematica
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We study a nonconventional ergodic average for asymptotically abelian weakly mixing C*-dynamical systems, related to a second iteration of Khinchin's recurrence theorem obtained by Bergelson in the measure-theoretic case. A noncommutative recurrence theorem for such systems is obtained as a corollary.
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.
Jian Li (2012)
Fundamenta Mathematicae
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We set up a general correspondence between algebraic properties of βℕ and sets defined by dynamical properties. In particular, we obtain a dynamical characterization of C-sets, i.e., sets satisfying the strong Central Sets Theorem. As an application, we show that Rado systems are solvable in C-sets.
A. N. Sharkovskii (1989)
Banach Center Publications
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Terrence Adams (2015)
Colloquium Mathematicae
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A technique is presented for multiplexing two ergodic measure preserving transformations together to derive a third limiting transformation. This technique is used to settle a question regarding rigidity sequences of weak mixing transformations. Namely, given any rigidity sequence for an ergodic measure preserving transformation, there exists a weak mixing transformation which is rigid along the same sequence. This establishes a wide range of rigidity sequences for weakly mixing dynamical...
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.
Sergiĭ Kolyada, Oleksandr Rybak (2013)
Colloquium Mathematicae
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We introduce and study the Lyapunov numbers-quantitative measures of the sensitivity of a dynamical system (X,f) given by a compact metric space X and a continuous map f: X → X. In particular, we prove that for a minimal topologically weakly mixing system all Lyapunov numbers are the same.
Ou, Baiyu, Liu, Desheng (2010)
Discrete Dynamics in Nature and Society
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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...
Miguel A. F. Sanjuán (1992)
Acta Universitatis Carolinae. Mathematica et Physica
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Andrzej Pelczar (1989)
Banach Center Publications
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N. N. Chentsova (1989)
Banach Center Publications
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Anishchenko, Vadim S., Strelkova, Galina I. (1998)
Discrete Dynamics in Nature and Society
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Awadalla, Attia.A. (2006)
APPS. Applied Sciences
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