Dynamics Day: 8 June at 10:00, ICTP LB Seminar Room D

[ICTP Math Section]

*MATH Seminars:  Dynamics Day*

*Date and Venue*: Monday 8 June at 10:00 - ICTP Leonardo Building, 
Seminar Room D

*Programme:*
*
*

  * 10:00 - 10:30 *Jernej Činč *(University of Maribor and ICTP)

*/Dynamics on Fences/*

*Abstract:*
Homeomorphisms of the Cantor set play a fundamental role in topology, 
dynamical systems, and descriptive set theory, where they are studied 
from different perspectives. Recently, various properties of so-called 
fence-like objects have attracted attention. Several recent works 
investigate both the structure of these spaces and the dynamics of 
homeomorphisms defined on them. In this work, we develop a general 
technique that allows one to transfer—or lift—the dynamics of a given 
homeomorphism of the Cantor set to a homeomorphism of a fence of the 
types described above. This is joint work with Udayan B. Darji 
(University of Louisville) and Benjamin Vejnar (Charles University).

  * 10:35 - 11:05 *Rubio Gunawan *(SISSA and ICTP)

*/Smooth Circle Covering with a Physical Measure on a Hyperbolic 
Repelling Fixed Point/*

*Abstract:*
We construct an example of a smooth (C-infinity) circle covering map 
topologically conjugate to the doubling map, such that it has a physical 
measure supported on a hyperbolic repelling fixed point. A key technical 
step is a realization method of independent interest, which gives a 
canonical way to construct a full branch map given its induced map.

  * 11:05 - 11:15 *Coffee Break*

  * 11:15 - 12:00 *Yakov Pesin *(Pennsylvania State University)

*/Is the set of Birkhoff generic points big?/*

*Abstract:*
By the classical Birkhoff Ergodic Theorem, given a homeomorphism of a 
compact metric space and a continuous function, the set of Birkhoff 
generic points of this function has full measure with respect to any 
invariant measure and hence, it is “big” from the measure-theoretical 
point of view. However, the situation becomes more complicated (and 
interesting) if we use other characteristics to “measure” this set such 
as its Hausdorff dimension and its topological entropy. I will discuss 
some well-known and less-known recent results in this direction. I will 
also consider the topological structure of this set and illustrate that 
under some mild and natural conditions this set is of the 1-st Baire 
category and hence is “small” from the topological point of view.

To attend via *Zoom* please register here: 
https://zoom.us/meeting/register/lh0rNHAFRSWryeuWgOZ1Rw

All are welcome to join.

-- 
Micol Stock
Secretariat of the ICTP Math Section

Abdus Salam International Centre for Theoretical Physics
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34151 Trieste
Italy

Tel.: (+39) 040 2240 4455