seminar: Perturbations of dynamical systems with additive noise, noise induced order and linear response
speaker: Laurent Vuillon (University Savoie Mont Blanc)abstract: In the first part of this talk, we focus on discrete dynamical systems and symbolic dynamics in particular for constructing Sturmian and Christoffel words. These words appears naturally in discrete geometry as a coding of discrete lines and discrete segments. We study their structures using continued fraction expansions and combinatorial properties.
In the second part, we introduce the Markoff numbers which are fascinating integers related to number theory, Diophantine equation, hyperbolic geometry, continued fractions and Christoffel words. Many great mathematicians have worked on these numbers and the 100 years famous uniqueness conjecture by Frobenius is still unsolved. We state a new formula to compute the Markoff numbers using iterated palindromic closure and the Thue-Morse substitution. The main theorem shows that for each Markoff number m, there exists a word v ∈ {a, b}∗ such that m − 2 is equal to the length of the iterated palindromic closure of the iterated antipalindromic closure of the word av. This construction gives a new recursive construction of the Markoff numbers by the lengths of the words involved in the palindromic closure.
timetable:
Wed 20 Feb, 14:30 - 15:30, Sala Conferenze Centro De Giorgi
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