C2 surface diffeomorphisms have symbolic extensions

• 成果类型: Article
• 署名作者: Burguet, David
• 署名单位: Universite Paris Saclay
• 刊物名称: INVENTIONES MATHEMATICAE
• ISSN/ISSBN: 0020-9910
• DOI: 10.1007/s00222-011-0317-8
• 发表日期: 2011
• 页码: 191-236
• 关键词: volume growth; entropy; PROOF

摘要

We prove that C-2 surface diffeomorphisms have symbolic extensions, i.e. topological extensions which are subshifts over a finite alphabet. Following the strategy of Downarowicz and Maass (Invent. Math. 176: 617-636, 2009) we bound the local entropy of ergodic measures in terms of Lyapunov exponents. This is done by reparametrizing Bowen balls by contracting maps in a approach combining hyperbolic theory and Yomdin's theory.