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Tuesday Seminar on Topology
Seminar information archive ～07/01｜Next seminar｜Future seminars 07/02～
| Date, time & place | Tuesday 17:00 - 18:30 056Room #056 (Graduate School of Math. Sci. Bldg.) |
|---|---|
| Organizer(s) | KOHNO Toshitake, KAWAZUMI Nariya, KITAYAMA Takahiro, SAKASAI Takuya |
| Remarks | Tea: 16:30 - 17:00 Common Room |
Next seminar
2022/07/05
17:00-18:00 Online
Pre-registration required. See our seminar webpage.
Yushi Nakano (Tokai University)
Non-existence of Lyapunov exponents for homoclinic bifurcations of surface diffeomorphisms (JAPANESE)
https://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index_e.html
Pre-registration required. See our seminar webpage.
Yushi Nakano (Tokai University)
Non-existence of Lyapunov exponents for homoclinic bifurcations of surface diffeomorphisms (JAPANESE)
[ Abstract ]
Lyapunov exponent is widely used in natural science including mathematics, such as a tool to find chaotic signal or a foundation of non-uniformly hyperbolic systems theory. However, its existence (outside of the supports of invariant probability measures) is seldom discussed. In this talk, I consider the problem of whether the Lyapunov irregular set, i.e. the set of points at which Lyapunov exponent fails to exist, has positive Lebesgue measure. I will show that surface diffeomorphisms with a robust homoclinic tangency given by Colli and Vargas, as well as other several known nonhyperbolic dynamics, has the Lyapunov irregular set of positive Lebesgue measure. This is a joint work with S. Kiriki, X. Li and T. Soma.
[ Reference URL ]Lyapunov exponent is widely used in natural science including mathematics, such as a tool to find chaotic signal or a foundation of non-uniformly hyperbolic systems theory. However, its existence (outside of the supports of invariant probability measures) is seldom discussed. In this talk, I consider the problem of whether the Lyapunov irregular set, i.e. the set of points at which Lyapunov exponent fails to exist, has positive Lebesgue measure. I will show that surface diffeomorphisms with a robust homoclinic tangency given by Colli and Vargas, as well as other several known nonhyperbolic dynamics, has the Lyapunov irregular set of positive Lebesgue measure. This is a joint work with S. Kiriki, X. Li and T. Soma.
https://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index_e.html
