Displaying similar documents to “On the genesis of symbolic dynamics as we know it”

Minimal sets of generalized dynamical systems

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.

Minimal sets of generalized dynamical systems

Basilio Messano, Antonio Zitarosa (1989)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

Similarity:

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.

Relatively independent joinings and subsystems of W*-dynamical systems

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.

The centralizer of Morse shifts

Mariusz Lemanczyk (1985)

Annales scientifiques de l'Université de Clermont-Ferrand 2. Série Probabilités et applications

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Generic points in the cartesian powers of the Morse dynamical system

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.