We investigate quantitative recurrence in systems having an infinite invariant measure. We extend the Ornstein–Weiss theorem for a general class of infinite systems estimating return time in decreasing sequences of cylinders. Then we restrict to a class of one-dimensional maps with indifferent fixed points and calculate quantitative recurrence in sequences of balls, obtaining that this is related to the behaviour of the map near the fixed points.
The recurrence time for ergodic systems with infinite invariant measures
GALATOLO, STEFANO;
2006-01-01
Abstract
We investigate quantitative recurrence in systems having an infinite invariant measure. We extend the Ornstein–Weiss theorem for a general class of infinite systems estimating return time in decreasing sequences of cylinders. Then we restrict to a class of one-dimensional maps with indifferent fixed points and calculate quantitative recurrence in sequences of balls, obtaining that this is related to the behaviour of the map near the fixed points.File in questo prodotto:
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