Attracting currents and equilibrium measures for quasi-attractors of

• 成果类型: Article
• 署名作者: Taflin, Johan
• 署名单位: Universite Bourgogne Europe
• 刊物名称: INVENTIONES MATHEMATICAE
• ISSN/ISSBN: 0020-9910
• DOI: 10.1007/s00222-018-0786-0
• 发表日期: 2018
• 页码: 83-137
• 关键词: polynomial diffeomorphisms; intersection theory; DYNAMICS; entropy; sets; ENDOMORPHISMS; exponents; MAPS

摘要

Let f be a holomorphic endomorphism of of degree d. For each quasi-attractor of f we construct a finite set of currents with attractive behaviors. To every such attracting current is associated an equilibrium measure which allows for a systematic ergodic theoretical approach in the study of quasi-attractors of . As a consequence, we deduce that there exist at most countably many quasi-attractors, each one with topological entropy equal to a multiple of . We also show that the study of these analytic objects can initiate a bifurcation theory for attracting sets.