CRM: Centro De Giorgi
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60 years of dynamics and number expansions

Ergodic and thermodynamic properties of Fibonacci unimodal maps

speaker: Henk Bruin (Universität Wien)

abstract: Unimodal maps of Fibonacci combinatorics were first described by Hofbauer and Keller as the most likely candidate to have a wild Cantor attractor. Although the quadratic Fibonacci map has an absolutely continuous invariant probability, Fibonacci maps of sufficiently high critical order were indeed to have an wild attractor, thus completing Milnor's picture of attractors and Lebesgue ergodic behaviour for unimodal interval maps. As such, Fibonacci maps display a rich behaviour, having finite, infinite or dissipative absolutely continuous invariant measures, depending on the critical order, with (attracting) Cantor set that factorizes over the golden mean circle rotation, which then can also be shown to be the maximal automorphic factor. Also the thermodynamic pressure function has been studied, and the most recent contribution (joint with Terhesiu and Todd) shows this as an interesting example of more general theory of how to estimate the shape of the pressure function near parameters with an infinite invariant measure.


timetable:
Fri 14 Dec, 12:15 - 13:00, Aula Dini
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