講演のタイトルと概要(新しい順に並べてあります)
Titles and Abstracts
- 12月9日(金)
場所, 時間:東京大学駒場キャンパス 数理科学研究科棟 15:00-18:00
- Xiaodong Wang 氏 (School of Mathematical Sciences, Shanghai Jiao Tong University)
- Hyperbolicity versus weak periodic orbits inside homoclinic classes
- Abstract:
-
We prove the “star” conjecture restricted to homoclinic classes. To be
precise, for
C^1-generic diffeomorphisms, if the periodic orbits contained in a
homoclinic class H(p)
have all their Lyapunov exponents bounded away from 0, then H(p) must
be (uniformly)
hyperbolic. This gives a way to characterize lack of hyperbolicity of homoclinic
classes through the existence of “weak” periodic orbits. The main
difficulty to be “restricted”
is that the homoclinic class H(p) is not known isolated in advance. Hence
the “weak” periodic orbits created by perturbations near the
homoclinic class have to
be guaranteed strictly inside the homoclinic class. We construct in
the proof several
perturbations which are not simple applications of the connecting lemmas.
- 10月14日(金)
場所, 時間:東京大学駒場キャンパス 数理科学研究科棟 126号室 15:00-18:00
- 山本 謙一郎 氏 (長岡技術科学大学)
- On the one-way specification property and its applications
- Abstract:
-
この講演ではspecification propertyを一般化したone-way
specification propertyという性質を導入し,それをみたすいくつかの1次元
力学系の例を紹介する.また,この性質の応用として,これらの力学系,
特にsoficなnegative beta-transformation,がルベーグ測度をリファーレンス
測度として大偏差原理をみたすことを示す.
- 6月17日(金)
場所, 時間:東京大学駒場キャンパス 数理科学研究科棟 126号室 13:00-15:00
- Warwick Tucker 氏 (Uppsala University, Sweden)
- (講演1) Set-valued numerics and the n-body problem
- Abstract:
-
We give a short introduction to set-valued numerics - the
foundation of rigorous computations. These techniques are applied to the
classical problem in Newtonian n-body of determining the number of
relative equlibria a set of planets can display. Some partial results
for the restricted 3-body problem are discussed, as well as future
goals. This is joint work with Piotr Zgliczynski.
- (講演2) In search for the Hénon attractor
- Abstract:
-
By performing a systematic study of the Hénon map, we find
low-period sinks for parameter values extremely close to the classical
ones. This raises the question whether or not the well-known Hénon
attractor is a strange attractor, or simply a stable periodic orbit.
Using results from our study, we conclude that even if the latter were
true, it would be practically impossible to establish this by computing
trajectories of the map. This is joint work with Zbigniew Galias.
- 6月14日(火)
場所, 時間:一橋大学国立キャンパス 第2研究館1F 共同研究室 16:30-18:00
- Sulimon Sattari 氏 (UC Merced, USA)
- Computing chaotic transport rates using heteroclinic tangles
and periodic orbits
- Abstract:
-
The escape rate of asteroids, chemical reaction rates, and fluid mixing rates are
all examples of chaotic transport rates. One can typically launch
a Monte Carlo simulation over millions of trajectories and compute
such rates, however we seek to extract this information from a smaller
number of trajectories.
The homotopic lobe dynamics technique uses the topological forcing of
stable and unstable manifolds of saddle points to compute a system's
symbolic dynamics, which can be used to compute periodic orbits and
transport rates. I will demonstrate this technique by computing mixing
rates in a fluid system and the ionization rate for a classical atomic
system.
- 5月27日(金)
場所, 時間:東京大学駒場キャンパス 数理科学研究科棟 122号室 15:00-18:00
- 松元 重則 氏(日本大学)
- Dynamics of the horocycle and geodesic flows of compact foliations by hyperbolic surfaces
- Abstract:
-
各葉が双曲的曲面であるような葉層構造を閉多様体上に考える。
その葉の方向の単位接ベクトルの全体のなす空間の上には、測地流、安定ホロサイクル流、
不安定ホロサイクル流が自然に定義される。これらの流れの力学的性質を論ずる。特に
(不)安定ホロサイクル流の各軌道が稠密になるために条件を探る。(Matilde Martinez,
Alberto Verjovsky との共同研究)
- 4月22日(金)
場所, 時間:東京大学駒場キャンパス 数理科学研究科棟 118号室 15:00-18:00
- Dmitry Turaev 氏(Imperial College, London)
- On wandering domains near homoclinic tangencies
- Abstract:
-
In a recent paper by Kiriki and Soma a solution to van Strien problem of
the existence of non-trivial wandering domains for two-dimensional
maps was proposed
for the case of finite smoothness. We discuss a possibility to extend
their results
to the real-analytic case and the case of three-dimensional polynomial
diffeomorphisms.
講演者を募集中です。
連絡先:
斉木 吉隆 (yoshi.saiki(at)r.hit-u.ac.jp)
〒186-8601 東京都国立市中2-1
一橋大学大学院商学研究科
高橋 博樹 (hiroki(at)math.keio.ac.jp)
〒223-8522 神奈川県横浜市港北区日吉3-14-1
慶應義塾大学理工学部数理科学科
林 修平 (shuhei(at)ms.u-tokyo.ac.jp)
〒153-8914 東京都目黒区駒場3-8-1
東京大学大学院数理科学研究科