seminar: Matching for a family of piecewise linear maps
speaker: Carlo Carminati (Università di Pisa)abstract: We consider a 1-parameter family (Qγ){γ ∈ ℝ} of piecewise linear maps, and we study how the metric entropy of Qγ depends upon the parameter γ. Despite the simple nature of the system, the behaviour of the entropy is quite surprising: it is smooth outside a zero measure set (but not everywhere), and its graph displays a complicated self-similar structure. We shall show that this phenomenon is due to a special combinatorial feature, called matching property, which was first detected for the family of α-continued fractions. Indeed, we belive that understanding the mechanisms which rule the behaviour of the entropy for this family of piecewise maps might help to give an answer to some open questions about the family of α-continued fractions. (This is a work in progress with H. Bruin, S. Marmi and A. Profeti and is performed in the framework of the PRIN 2010-2011 "Teorie geometriche e analitiche dei sistemi Hamiltoniani in dimensioni finite e infinite", code 2010JJ4KPA009).
timetable:
Wed 28 May, 17:00 - 17:45, Sala Conferenze Centro De Giorgi
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