Kyoto Dynamics Days 9

• 日時: 2010年3月8日(月) 14:30 -- 3月10日(水) 14:45

• 場所: 京都大学 大学院理学研究科 理学部３号館108講演室 (Kyoto Univ., Dept. of Math., Room 108)
  　　　〒606-8502 京都市左京区北白川追分町, 市バス京大農学部前下車
  　　　アクセス

プログラム PROGRAM

• 3月8日(月) Monday, March 8

  • 14:30-15:30 Jeff Xia (Northwestern University)
    Area-Preserving Surface Diffeomorphisms I

  • 16:00-17:00 David Blazquez-Sanz (Sergio Arboleda University/新潟大学[Niigata University])
    On the Dynamical Meaning of Picard-Vessiot Theory (講演ノート )

• 3月9日(火) Tuesday, March 9

  • 9:45-10:45 Jeff Xia (Northwestern University)
    Area-Preserving Surface Diffeomorphisms II

  • 11:00-12:00 柴山允瑠 (京都大学) [Mitsuru Shibayama (Kyoto Univ.)]
    A variational proof of the existence of Gerver's super-eight orbit in the four-body problem

  • 13:45-14:45 鷲見直哉 (東京工業大学) [Naoya Sumi (Tokyo Institute of Technology)]
    Empirical measures for partially hyperbolic diffeomorphisms

  • 15:00-16:00 David Blazquez-Sanz (Sergio Arboleda University/新潟大学[Niigata University])
    On the Relation between Differential Galois Theory and some Sturm-Liouville Problems

  • 16:15-17:15 Jeff Xia (Northwestern University)
    Foliations, topology and dynamics for partially hyperbolic diffeomorphisms I

  • 18:00-- 懇親会　Dinner (百万遍「門」にて)

• 3月10日(水) Wednesday, March 10

  • 9:45-10:45 Jeff Xia (Northwestern University)
    Foliations, topology and dynamics for partially hyperbolic diffeomorphisms II

  • 11:00-12:00 辻井正人 (九州大学) [Masato Tsujii (Kyushu Univ.)]
    Transfer operators for hyperbolic and partially hyperbolic diffeomorphisms

  • 13:45-14:45 Jeff Xia (Northwestern University)
    Foliations, topology and dynamics for partially hyperbolic diffeomorphisms III

****Area-Preserving Surface Diffeomorphisms*****

The study of area-preserving diffeomorphisms has a long history and it goes back to Poincaré who, among many other things, discovered the homoclinic phenomenon. Poincaré had also posed many problems, some of them remain unsolved until today. The most notable one is the so-called C^r closing lemma, which asks whether the set of periodic points is dense for a generic area-preserving diffeomorphism. A related problem is whether every hyperbolic periodic point has a transversal homoclinic point for a C^r generic area-preserving diffeomorphism. We will discuss these and related problems and some recent progresses.

****Foliations, topology and dynamics for partially hyperbolic diffeomorphisms****

We discuss the roles partial hyperbolicity plays in a given dynamical system; We will present several results on partially hyperbolic systems, particularly the ones with lower center dimensions. These results include: continuity properties of topological entropy, abundance of pathological foliations and entropy conjecture for systems with one dimensional center. One of the key ingredients in these results is a new class of topological invariants we introduced for invariant foliations.

David Blazquez-Sanz氏の１回目の講演のノートは以下のURLからダウンロードできます。
Blazquez-Sanz-Kyoto2010.pdf (PDF 312KB)

この研究集会は、京都大学グローバルＣＯＥプログラム 「数学のトップリーダーの育成- -コア研究の深化と新領域の開拓」（拠点リーダー　深谷賢治）、 および科学研究補助金「実および複素力学系の複素解析的研究」（代表者　宍倉光広）により開催されます。

9日の懇親会に出席される予定の方で、当日13:30までに会場に来られない方は 宍倉までご連絡ください。

連絡先(Organizer)： 宍倉 光広 (Mitsuhiro Shishikura)　
mitsu AT math DOT kyoto-u DOT ac DOT jp
〒606-8502 京都市左京区北白川追分町
京都大学大学院理学研究科数学教室
電話: 075-753-3738（研究室） 075-753-3700（事務室） FAX: 075-753-3711