ICTP MATHEMATICS SEMINAR - Thursday 13 June, at 16:00 - VENUE: Luigi Stasi seminar room - Yakov Pesin

[ICTP Math Section]

_ICTP MATHEMATICS SEMINARS 2024_

Thursday 13 June, at 16:00

VENUE: Luigi Stasi seminar room


Speaker: Yakov Pesin (Penn State University, USA)


Title: Dynamics Via Geometric Measure Theory


Abstract: I will introduce the concept of dimension structures in 
abstract spaces. Given such a space endowed with a dimension structure 
one can define various characteristics of dimension type and study their 
basic properties. I will discuss three major examples of dimension 
structures:
1) The dimension structure associated with metric in a metric space; the 
corresponding dimension characteristics are the classical Hausdorff and 
box dimensions of sets and measures.

2) The dimension structure associated with a metric and a Borel measure 
in a metric space; the corresponding dimension characteristics are the 
dimension spectra including the well-known Hentschel-Procaccia dimension 
spectrum.

3) The dimension structure associated with a dynamical system and a 
continuous function in a compact metric space; the corresponding 
dimension characteristics are the topological pressure of the function; 
this reveals the dimension nature of the topological pressure as well as 
topological and metric entropies which are the classical invariants of 
dynamics.

All are welcome to attend.

/https://indico.ictp.it/event/10743//

-- 
Koutou Mabilo
ICTP Mathematics Group
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