A transcendental dynamical degree

Abstract: 

The degree of a dominant rational map f:Pn→Pnf:Pn→Pn is the common degree of its homogeneous components.  By considering iterates of ff, one can form a sequence deg(fn)deg(fn), which is submultiplicative and hence has the property that there is some λ≥1λ≥1 such that (deg(fn))1/n→λ(deg(fn))1/n→λ.  The quantity λλ is called the first dynamical degree of ff.  We’ll give an overview of the significance of the dynamical degree in complex dynamics and describe an example in which this dynamical degree is provably transcendental.  This is joint work with Jeffrey Diller and Mattias Jonsson.

This talk is part of the online Number Theory Web Seminar, and will be streamed live on Zoom.

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Organisers:

Mike Bennett (University of British Columbia)

Philipp Habegger (University of Basel)

Alina Ostafe (UNSW Sydney)