セミナー

発表言語 日本語
開催日 2010年05月14日 14時00分
終了日 2010年05月14日 18時00分
開催場所京都大学理学部6号館609号室
セミナー名京都力学系セミナー
タイトル Finite resolution dynamics 
分野 幾何
解析
講演者名Pawel Pilarczyk
講演者所属University of Minho
概要We develop a new mathematical model for describing a dynamical system at limited resolution (or finite scale), and we give precise meaning to the notion of a dynamical system having some property at finite resolution. Open covers are used to approximate the topology of the phase space in a finite way, and the dynamical system is represented by means of a combinatorial multivalued map. We translate notions of transitivity and mixing known for general dynamical systems into the finite setting. Moreover, we formulate equivalent conditions for these properties in terms of graphs, and provide effective algorithms for their verification. As an application we show that the H\'enon attractor is topologically mixing at all resolutions coarser than $10^{-5}$. This is joint work with Stefano Luzzatto.
リンクhttps://www.math.kyoto-u.ac.jp/dynamics/