2015 Fiscal Year Final Research Report
On the characterization of measureexpansive differentiable dynamical systems
Project/Area Number 
25400105

Research Category 
GrantinAid for Scientific Research (C)

Allocation Type  Multiyear Fund 
Section  一般 
Research Field 
Basic analysis

Research Institution  Utsunomiya University 
Principal Investigator 

Project Period (FY) 
20130401 – 20160331

Keywords  力学系理論 / 拡大性 / 確率測度 / 双曲性 / 占有的分解 
Outline of Final Research Achievements 
In this research project, we consider the sets of diffeomorphisms which are measureexpansive for any probability measure, invariant probability measure and ergodic measure, and study the sets from the viewpoint of geometric theory of dynamical systems. It is proved that the C1interior of the set of measureexpansive diffeomorphisms for any probability measure is quasiAnosov systems and C1interior of the set of measureexpansive diffeomorphisms for any invariant probability measures is Ωstable systems. Furthermore, it is also proved that there exists a nonempty C1open set of robustly nonhyperbolic and transitive diffeomorphisms such that each element of the set is measure expansive for any ergodic measure.

Free Research Field 
擬軌道尾行性や拡大性を持つ力学系の特徴付け
