Generic hyperbolicity of Aubry sets on surfaces

• 成果类型: Article
• 署名作者: Contreras, G.; Figalli, A.; Rifford, L.
• 署名单位: University of Texas System; University of Texas Austin; Universite Cote d'Azur
• 刊物名称: INVENTIONES MATHEMATICAE
• ISSN/ISSBN: 0020-9910
• DOI: 10.1007/s00222-014-0533-0
• 发表日期: 2015
• 页码: 201-261
• 关键词: mather sets; REGULARITY; EXISTENCE

摘要

Given a Tonelli Hamiltonian of class on the cotangent bundle of a compact surface, we show that there is an open dense set of potentials in the topology for which the Aubry set is hyperbolic in its energy level.