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Fractal entropy of
nonautonomous systems
Rui Kuang, Wen-Chiao Cheng and Bing Li |
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Vol. 262 (2013), No. 2, 421–436
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Abstract |
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We define formulas of entropy dimension for a nonautonomous dynamical system consisting of a sequence of continuous self-maps of a compact metric space. This study reveals analogues of basic propositions for entropy dimension, such as the power rule, product rule and commutativity, etc. These properties allow us to convert to an equality an inequality found by de Carvalho (1997) concerning the product rule for the autonomous dynamical system. We also prove a subadditivity rule of entropy dimension for one-dimensional dynamics based on our previous work. |
Keywords
entropy dimension, dynamical systems, nonautonomous
dynamical systems, power rule, product rule, commutativity,
subadditivity
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Mathematical Subject Classification 2000
Primary: 37D35
Secondary: 37A35
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Milestones
Received: 9 February 2012
Revised: 12 August 2012
Accepted: 16 October 2012
Published: 16 April 2013
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Authors |
| Rui Kuang | |
| Department of Mathematics South China University of Technology 510641 Guangzhou China |
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| Wen-Chiao Cheng | |
| Department of Applied
Mathematics Chinese Culture University Yangmingshan, Taipei 11114 Taiwan |
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| Bing Li | |
| Department of Mathematics South China University of Technology 510641 Guangzhou China |
Department of Mathematical
Science University of Oulu P.O. Box 3000 FI-90014 Oulu Finland |
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