| Budget Amount *help |
¥4,940,000 (Direct Cost: ¥3,800,000、Indirect Cost: ¥1,140,000)
Fiscal Year 2016: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2015: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2014: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Fiscal Year 2013: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
|
|---|
| Outline of Final Research Achievements |
We give an answer to a smooth version of the open problem of Takens in [Nonlinearity 21 (3) (2008) T33--T36.] which is related to historic behavior of dynamical systems. To obtain the answer, we show the existence of non-trivial wandering domains near a homoclinic tangency, which is conjectured by Colli-Vargas [Ergod. Th. Dynam. Sys. 21 (2001) 1657--1681].
Concretely speaking, it is proved that any Newhouse open set in the space of smooth diffeomorphisms on a closed surface is contained in the closure of the set of diffeomorphisms which have non-trivial wandering domains whose forward orbits have historic behavior. Moreover, this result implies an answer in the smooth category to one of the open problems of van Strien [Discrete Contin. Dyn. Syst. 27 (2) (2010) 557--588] which is concerned with wandering domains for Henon family.
|
