Mini-course

Lecturers: Henk Bruin (Vienna) and Mike Todd (St Andrews)

Title: Inducing Techniques in Thermodynamic Formalism.

Abstract: The theory of thermodynamic formalism was introduced into dynamics by Sinai, Ruelle and Bowen, initially for hyperbolic systems, to give the ideas of thermodynamic pressure, equilibrium states and phase transitions on a mathematical basis. Non-(uniformly) hyperbolic system can frequently be accelerated so as to produce a hyperbolic system (with usually countably many branches), and this technique is called inducing. It requires particular adaptations which will be discussed in this course, especially for maps of the interval and symbolic (sub)shift systems.

Topics to be covered include:

• basic notions of thermodynamic formalism and phase transitions.
• shift spaces, substitution shifts.
• relevant notions of interval dynamics.
• aspects of hyperbolic expanding maps with countably many branches.
• applications to multifractal analysis.
• physics motivation with quasi-crystals.

Program

There will be introductory talks aimed at students and non-specialists on Thursday's evening (20 November). There will be other talks, but we would like to not overload the program.

Venue

All lectures will take place at the Faculty of Applied Mathematics at the AGH University of Science and Technology in Krakow (wms.agh.edu.pl)

Registration

There will be no conference fee, but we do ask people to register in advance. It is probable that we will be able to cover the accommodation of some number of participants (with the strong emphasis of young people and researchers without financial support of their organizations).

About

Wandering seminar is an initiative, which aims at integrating ergodic theory and dynamical systems research groups in Poland. The idea is to organise mini-conferences/workshops a few times each year. These meeting are to be devoted to actual research topics in our area. Contrary to what the title suggest, this should be a recurring event, which only wanders geographically across Polish universities with dynamical systems research groups. This will be the third meeting of the Wandering Seminar (the first was in January in Krakow and second in April in Warszawa).

Organizers

• Dominik Kwietniak (UJ)
• Piotr Oprocha (AGH)
• Michal Rams (IMPAN)

Partners