Dynamical systems which realize given random bi-sequences of points on their orbits

A dynamical system consists of a phase space of possible states, together with an evolution rule that determines all future states and all past states given a state at any particular moment. In this paper, we show that for any countable random infinite bi-sequences of states of some phase space, the...

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Bibliographic Details
Published in:Topology and its applications 2011-06, Vol.158 (9), p.1163-1171
Main Author: Kato, Hisao
Format: Article
Language:English
Subjects:
Chaotic
Dynamical system
Flow
Good measure
Measure-preserving homeomorphism
Orbits
Transitive homeomorphism
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Summary:A dynamical system consists of a phase space of possible states, together with an evolution rule that determines all future states and all past states given a state at any particular moment. In this paper, we show that for any countable random infinite bi-sequences of states of some phase space, there exists an evolution rule in C 0 -topology which realizes precisely the given sequences of states on their orbits and satisfies some regular conditions on the times to realize the states.
ISSN:0166-8641
1879-3207
DOI:10.1016/j.topol.2011.04.004