In this paper,local unstable metric entropy,local unstable topological entropy and local unstable pressure for partially hyperbolic endomorphisms are introduced and investigated.Specially,two variational principles co...In this paper,local unstable metric entropy,local unstable topological entropy and local unstable pressure for partially hyperbolic endomorphisms are introduced and investigated.Specially,two variational principles concerning relationships among the above mentioned numbers are formulated.展开更多
Katok’s entropy formula is an important formula in entropy theory.It plays significant roles in large deviation theories,multifractal analysis,quantitative recurrence and so on.This paper is devoted to establishing K...Katok’s entropy formula is an important formula in entropy theory.It plays significant roles in large deviation theories,multifractal analysis,quantitative recurrence and so on.This paper is devoted to establishing Katok’s entropy formula of unstable metric entropy which is the entropy caused by the unstable part of partially hyperbolic systems.We also construct a similar formula which can be used to study the quantitative recurrence in the unstable manifold for partially hyperbolic diffeomorphisms.展开更多
基金supported by the National Natural Science Foundation of China (Nos. 11771118,11801336, 12171400)the Innovation Fund Designated for Graduate Students of Hebei Province (No.CXZZBS2018101)+1 种基金China Scholarship Council (CSC for short)China Postdoctoral Science Foundation (No. 2021M691889).
文摘In this paper,local unstable metric entropy,local unstable topological entropy and local unstable pressure for partially hyperbolic endomorphisms are introduced and investigated.Specially,two variational principles concerning relationships among the above mentioned numbers are formulated.
基金supported by NNSF of China(12101446,11401581,11971236)The second author was supported by NNSF of China(11401581)+1 种基金the third author was supported by NNSF of China(11671208,11431012)At the end,we would like to express our gratitude to Tianyuan Mathematical Center in Southwest China,Sichuan University and Southwest Jiaotong University for their support and hospitality.
文摘Katok’s entropy formula is an important formula in entropy theory.It plays significant roles in large deviation theories,multifractal analysis,quantitative recurrence and so on.This paper is devoted to establishing Katok’s entropy formula of unstable metric entropy which is the entropy caused by the unstable part of partially hyperbolic systems.We also construct a similar formula which can be used to study the quantitative recurrence in the unstable manifold for partially hyperbolic diffeomorphisms.
