Regularity and bifurcation phenomena in simple families of maps

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Date(s) - 19/05/2015
11 h 00 min - 12 h 00 min


We consider a 1-parameter family (Q_γ)_{γ ∈ ℝ} of piecewise linear maps, and we study how the metric entropy of Q_γ 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.
(This is a joint work with H. Bruin, S. Marmi and A. Profeti).


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