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Variational
inequality for conditional pressure on a Borel subset
Yuan Li, Ercai Chen and Wen-Chiao Cheng |
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Vol. 256 (2012), No. 1, 151–164
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Abstract |
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We define topological conditional pressure on a Borel subset and investigate its properties. We then estimate the supremum of metric conditional entropy with potential energy. The usual basic properties hold for this topological conditional pressure. In particular, we find a variational inequality that is an extension of the variational principle for topological pressure. |
Keywords
variational principle, topological conditional pressure,
conditional entropy
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Mathematical Subject Classification 2010
Primary: 37A35, 37B40
Secondary: 37D35
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Milestones
Received: 3 March 2011
Revised: 9 November 2011
Accepted: 14 February 2012
Published: 6 May 2012
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Authors |
| Yuan Li | |
| Key Laboratory of Virtual Geographic
Environment Nanjing Normal University Nanjing, 210046 China |
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| Ercai Chen | |
| School of Mathematical Science Nanjing Normal University Nanjing, 210093 China |
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| Wen-Chiao Cheng | |
| Department of Applied
Mathematics Chinese Culture University Yangmingshan, Taipei 11114 Taiwan |
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