過去のセミナー: 2004年度, 2003年度, 2002年度, 2001年度
新しい順に並べてあります。
アブストラクト:
相馬 輝彦氏とMing-Chia Li氏との共同研究で、
Newhouseの予想 [S. Newhouse, ETDS, 24 (2004) no.5, 1725-1738]
に対し、例外的な場合を除き肯定的な解を得たので、
それを経緯も含めて報告する.
アブストラクト:
Fathi (1980) 及び R.Berlanga (2003) による
測度の空間 と 測度を保つ同相写像の群に関する仕事を紹介し,
さらに,僕の仕事と合わせて得られる
非コンパクト 2次元多様体の測度を保つ同相写像の群に関する結果を紹介する.
Abstract:
Recently, B. Malgrange propose a new point of view on
differential galois theory. Using differential geometry and
pseudogroup theory, he extend the theoryto a galois theory of
foliation.
These ideas can be used to define a kind of "galoisian
envelope" for an rational self-mapping f :X-->X . This
"envelope" is a singular Lie pseudogroup acting on X. When it
is not the pseudogroup the one of all the local
biholomorphisms of X, the map f is called special.
Using elementary dynamics and pseudogroup theory on CP^1, one
can prove that the special map are the integrable ones
(monomes, tchebitchev polynomial and Lattes examples).
We don't know if this result can be generalized in highter
dimension.
Abstract:
Mathematics is the study of patterns and pattern processes, and
dynamical systems theory traditionally has provided models for
pattern formation processes, or morphogenesis. The computer
revolution has produced radically new models, generalizing
those of partial differential equations, for example.
In this talk we will explore some of these new modeling
strategies, with applications to synchronization, emergence,
morphogenesis. We may touch upon -- and view graphics and
animations of -- chaotic (fractal) attractors, bifurcations,
and applications to various arts and sciences.
連絡先:
稲生 啓行
〒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