Πέμπτη 14 Οκτωβρίου, 11:15 – 12:00, Αίθουσα Μ2 (η ομιλία θα γίνει δια ζώσης).
Ομιλήτρια: Natalia Jurga, University of St Andrews
Τίτλος: Random matrix products and self-projective sets
Περίληψη: A finite set of matrices A⊂SL(2,ℝ) acts on one-dimensional real projective space (identified with the circle S1) through its linear action on ℝ2. In this talk we will be interested in the limit set; the smallest closed subset of S1 which contains all attracting and neutral fixed points of matrices belonging to the semigroup generated by A. Recently, Solomyak and Takahashi studied the Hausdorff dimension of the limit set under two assumptions: uniformly hyperbolicity (products of matrices from A grow in norm at a uniform exponential rate) and the Diophantine property (the semigroup generated by A is “far” from being a free semigroup). In this talk we will discuss an extension of their results beyond the uniformly hyperbolic setting. This is based on joint work with Argyrios Christodoulou.