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2009•Bulletin of the Russian Academy of Sciences PhysicsRequires access

Classification of one-dimensional chaotic models

Valery Mikhailovich Anikin, С. С. Аркадакский, S. N. Kuptsov, Alexander S. Remizov

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Abstract

Classifying chaotic maps using the relation between a map and its conjugate basic map with uniform invariant distribution is suggested. It is shown that every symmetric one-dimensional chaotic map with two monotonic branches is topologically equivalent to a tent map or a Bernoulli shift. An algorithm for finding a function conjugating two maps is formulated.

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Classifying chaotic maps using the relation between a map and its conjugate basic map with uniform invariant distribution is suggested. It is shown that every symmetric one-dimensional chaotic map with two monotonic branches is topologically equivalent to a tent map or a Bernoulli shift. An algorithm for finding a function conjugating two maps is formulated.

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Available abstract

Classifying chaotic maps using the relation between a map and its conjugate basic map with uniform invariant distribution is suggested. It is shown that every symmetric one-dimensional chaotic map with two monotonic branches is topologically equivalent to a tent map or a Bernoulli shift. An algorithm for finding a function conjugating two maps is formulated.

Key concepts: Chaotic, Chaotic map, Monotonic function, Bernoulli's principle, Topological conjugacy, Invariant (physics), Mathematics, Relation (database)

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