EVENT DETAILS AND ABSTRACT

Title: Monotonicity of entropy for real quadratic rational maps
Speaker: Khashayar Filom
Speaker Info: Northwestern University
Brief Description:
Special Note:
Abstract:

There is an extensive literature on the entropy behavior of polynomial interval maps as they vary in families. In particular, the monotonicity problem which asks about the connectedness of the level sets of the entropy function (the isentropes) has been of immense interest and is very well studied in the context of polynomial interval maps of full modality. In the much broader context of rational maps a real entropy function can be set up on the space of Möbius conjugacy classes of real rational maps. We chiefly focus on the case of degree two maps where there is an explicit description of the moduli space of real quadratic rational maps due to Milnor. This space admits a natural partition to several regions based on the modality and the degree of the restriction of ambient rational maps to the real circle. We will establish the monotonicity over some of these regions and present empirical evidence for its failure over certain another region.