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Dynamically defined recurrence dimension

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  • We modify the idea of a previous article [8] and introduce polynomial and exponential dynamically defined recurrence dimensions, topological invariants which express how the Poincaré recurrence time of a set grows when the diameter of the set shrinks. We introduce also the concept of polynomial entropy which applies in the case that topological entropy is zero and complexity function is polynomial. We compare recurrence dimensions with topological and polynomial entropies, evaluate recurrence dimensions of Sturmian subshifts and show some examples with Toeplitz subshifts.
    Mathematics Subject Classification: 37B20, 37B40, 37C45, 37B10.


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