Maximal entropy measures for piecewise affine surface homeomorphisms
2009 ◽
Vol 29
(6)
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pp. 1723-1763
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Keyword(s):
AbstractWe study the dynamics of piecewise affine surface homeomorphisms from the point of view of their entropy. Under the assumption of positive topological entropy, we establish the existence of finitely many ergodic and invariant probability measures maximizing entropy and prove a multiplicative lower bound for the number of periodic points. This is intended as a step towards the understanding of surface diffeomorphisms. We proceed by building a jump transformation, using not first returns but carefully selected ‘good’ returns to dispense with Markov partitions. We control these good returns through some entropy and ergodic arguments.
2011 ◽
Vol 32
(5)
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pp. 1783-1800
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Keyword(s):
2018 ◽
Vol 20
(4)
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pp. 408-418
2013 ◽
Vol 34
(6)
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pp. 1770-1793
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Keyword(s):
2011 ◽
Vol 32
(1)
◽
pp. 63-79
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1995 ◽
Vol 78
(3-4)
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pp. 815-825
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2016 ◽
Vol 18
(05)
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pp. 1550083
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2013 ◽
Vol 34
(5)
◽
pp. 1503-1524
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