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講演会
過去の記録 ～04/26｜次回の予定｜今後の予定 04/27～
2014年03月12日(水)
10:15-11:45 数理科学研究科棟(駒場) 470号室
Michele Triestino 氏 (Ecole Normale Superieure de Lyon)
Invariant distributions for circle diffeomorphisms of
irrational rotation number and low regularity (ENGLISH)
Michele Triestino 氏 (Ecole Normale Superieure de Lyon)
Invariant distributions for circle diffeomorphisms of
irrational rotation number and low regularity (ENGLISH)
[ 講演概要 ]
The main inspiration of this joint work with Andrés Navas is the beautiful result of Ávila and Kocsard: if f is a C^\\infty circle diffeomorphism of irrational rotation number, then the unique invariant probability measure is also the unique (up to rescaling) invariant distribution.
Using conceptual geometric arguments (Hahn-Banach...), we investigate the uniqueness of invariant distributions for C^1 circle diffeomorphisms of irrational rotation number, with particular attention to sharp regularity.
We prove that If the diffeomorphism is C^{1+bv}, then there is a unique invariant distribution of order 1. On the other side, examples by Douady and Yoccoz, and by Kodama and Matsumoto exhibit differentiable dynamical systems for which the uniqueness does not hold.
The main inspiration of this joint work with Andrés Navas is the beautiful result of Ávila and Kocsard: if f is a C^\\infty circle diffeomorphism of irrational rotation number, then the unique invariant probability measure is also the unique (up to rescaling) invariant distribution.
Using conceptual geometric arguments (Hahn-Banach...), we investigate the uniqueness of invariant distributions for C^1 circle diffeomorphisms of irrational rotation number, with particular attention to sharp regularity.
We prove that If the diffeomorphism is C^{1+bv}, then there is a unique invariant distribution of order 1. On the other side, examples by Douady and Yoccoz, and by Kodama and Matsumoto exhibit differentiable dynamical systems for which the uniqueness does not hold.
