Kyoto Dynamics Day 12

日時 (Date) :

2013年3月24日(日) (24 March, 2013) 10:30-16:40

会場 (Place) :

京都大学 大学院理学研究科 理学部３号館110講演室 (Kyoto Univ., Building No. 3, Room 110)
当日は3号館玄関は施錠されているため， 中庭，または110室南側の入口からお入りください．
〒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/ Access

講演者 (Speaker) :

Dimitry Turaev 氏（Imperial College London)

篠原 克寿 氏 (Katsutoshi Shinohara, 京都大学，Universite de Bourgogne)

プログラム PROGRAM

10:30-11:30 Turaev (1)

Lorenz attractors for flows and diffeomorphisms

(11:30-13:00 Lunch)

13:00-14:00 Shinohara (1)

An example of Iterated function systems on the interval with minimal cantor set

14:20-15:20 Turaev (2)

Fermi acceleration in time-dependent billiards

15:40-16:40 Shinohara (2)

Yet another example of C^1-wild diffeomorphisms

(18:00- Dinner)

24日の18時より懇親会を行います．当日の昼までに懇親会参加者の受付をするので， 午後から研究集会に参加される方は事前に浅岡まで連絡をお願いします．

アブストラクト Abstracts

Dimitry Turaev 氏

(1) "Lorenz attractors for flows and diffeomorphisms"

We generalise the classical theory of Lorenz attractors based on two notions: volume-hyperbolicity and chain-transitivity. The theory extends to time-periodic perturbations of systems with a Lorenz attractor, to lattices of weakly coupled systems of this type, and other examples. We show that Newhouse wild hyperbolic sets and Bonatti-Diaz blenders can be atypical constituent of higher-dimensional analogues of the Lorenz attractor. We also discuss local and global bifurcations that create Lorenz attractors and their higher-dimensional analogues.

(2) "Fermi acceleration in time-dependent billiards"

We discuss a novel theory of the evolution of energy in billiards with slowly moving boundaries, based on the Anosov-Kasuga theory of adiabatic invariants. We propose a stochastic description for the energy evolution, and demonstrate that the ergodicity of the billiard impedes the energy transfer from the moving boundary to the particle inside the billiard. We describe recent examples of time-dependent billiards for which a controlled violation of ergodicity leads to an exponential energy growth, i.e. to the effective energy transfer which is much more effective than in the ergodic case. We argue that the effect is of a fairly general nature: the periodic violation of ergodicity must be the key mechanism behind the energy flow from slow to fast degrees of freedom in slow-fast Hamiltonian systems with chaotic behaviour in the fast variables.

篠原克寿氏 (Katsutoshi Shinohara) :

"An example of Iterated function systems on the interval with minimal cantor set"

We consider IFSs on the interval with overlaps. We say that a compact set is minimal if every point has dense orbit in it. In general, it is not easy to determine the topology of the minimal set. In this talk, I give one explicit example of IFS for which we can see that it is a cantor set.

"Yet another example of C^1-wild diffeomorphisms"

A diffeomorphism is called tame if every chain recurrence class of itis robustly isolated, and a diffeomorphism is called wild if it is "far away" from tame diffeomorphisms (roughly speaking, wildness implies the frequent bifurcation which produces infinitely many chain recurrence classes).
In this talk, I will construct new types of wild diffeomorphisms. Their eminent novelty is that they exhibit certan kind of partial hyperbolicity, which tells us that the mechanis of their wildeness is different from that of Newhouse phenomena.