Infinite Interval Exchange Transformation with Positive Entropy
Teturo Kamae (1977)
Publications mathématiques et informatique de Rennes
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Teturo Kamae (1977)
Publications mathématiques et informatique de Rennes
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Gselmann, Eszter (2008)
Banach Journal of Mathematical Analysis [electronic only]
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Magda Komorníková, Jozef Komorník (1982)
Mathematica Slovaca
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Tomasz Downarowicz, Jacek Serafin (2002)
Fundamenta Mathematicae
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We consider a pair of topological dynamical systems on compact Hausdorff (not necessarily metrizable) spaces, one being a factor of the other. Measure-theoretic and topological notions of fiber entropy and conditional entropy are defined and studied. Abramov and Rokhlin's definition of fiber entropy is extended, using disintegration. We prove three variational principles of conditional nature, partly generalizing some results known before in metric spaces: (1) the topological conditional...
Chakrabarti, C.G., De, Kajal (2000)
International Journal of Mathematics and Mathematical Sciences
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Philippe Bénilan, Jose Carrillo, Petra Wittbold (2000)
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
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Riečan, B.
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Magda Komorníková, Jozef Komorník (1983)
Mathematica Slovaca
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Tao, Ming, Cheng, Zhixin, Yan, Jin (2007)
Revista Colombiana de Matemáticas
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Brunon Kamiński, José de Sam Lazaro (2000)
Colloquium Mathematicae
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We investigate the properties of the entropy and conditional entropy of measurable partitions of unity in the space of essentially bounded functions defined on a Lebesgue probability space.
Young-Ho Ahn, Dou Dou, Kyewon Koh Park (2010)
Studia Mathematica
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Recently the notions of entropy dimension for topological and measurable dynamical systems were introduced in order to study the complexity of zero entropy systems. We exhibit a class of strictly ergodic models whose topological entropy dimensions range from zero to one and whose measure-theoretic entropy dimensions are identically zero. Hence entropy dimension does not obey the variational principle.