Starts 8 Jun 2026 10:00
Ends 8 Jun 2026 14:00
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Math Seminars: Dynamics Day
ICTP
Leonardo Building - Lecture Room D
- 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).
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.
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.
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
https://zoom.us/meeting/register/lh0rNHAFRSWryeuWgOZ1Rw