[geometry-ml:01415] DCS セミナー開催のお知らせ

[Yuki Miura]

　　第19回　DCSセミナー　(Dynamics of Complex Systems)　のお知らせ
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講演者：　Prof. Yakov Pesin　(Pennsylvania State Univ.)
日　時：　3月12日(月)　15：00- 
場　所：　北海道大学理学部３号館３−２０５　
       
a) Title: "Thermodynamics of towers and the liftability problem"

Abstract: Thermodynamic formalism of statistical physics is a collection of results aimed at producing some "natural" invariant measures with strong ergodic properties　including Sinai-Ruelle-Bowen measures (absolutely continuous invariant measures in the one-dimensional case), measures of maximal dimension and entropy. In particular,one can study the pressure function, which plays crucial role in multifractal analysis and in applications to number theory. In the classical situations (Anosov maps, hyperbolic attractors, etc.) thermodynamical formalism can be effected using symbolic representations of these systems via subshifts of finite type.
 Many non-classical situations (e.g., one-dimensional unimodal maps and Henon attractors) can be handled using symbolic representations via towers whose base is the Bernoulli shift　on a countable set of states. I will describe general tower constructions and present some recent results on thermodynamics of the corresponding systems and in particular, on the study of the pressure function. The principle new phenomenon is that one may have to reduce the class of invariant measures under consideration to the so-called liftable measures. I will describe these measures and discuss the associated liftability problem.


b) Title: "A general approach for constructing SRB-measures for chaotic attractors"

Abstract: I discuss a general approach to the existence of SRB measures for local diffeomorphisms possessing chaotic attractors. I introduce a certain recurrence condition on the iterates of Lebesgue measure called “usable hyperbolicity” that is a version of Lyapunov?Perron regularity in the dissipative case. I will show that if the asymptotic rate of usable hyperbolicity is non-zero on a set of positive Lebesgue measure, then the system has an SRB measure. Some examples will be discussed.

DCSセミナーウェブ

http://www.math.sci.hokudai.ac.jp/center/field/seminar-index/seminar19.php

 DCS (Dynamics of Complex Systems)セミナーは、
「数学的予測方式の可能性と諸分野からのニーズを探る」という目的のもとで、
北大数学教室、数学連携研究センター、電子科学研究所、創成研究機構に所属する
力学系と周辺分野に関わるメンバーを中心に定期的に開催していく予定です。　


問い合わせ先：

由利美智子　yuri ＠ math.sci.hokudai.ac.jp
行木孝夫　nami ＠ math.sci.hokudai.ac.jp