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Invariant Currents for Surface Maps with Transcendental First Dynamical Degree

Adventurous Berkeley Complex Dynamics May 02, 2022 - May 06, 2022

May 06, 2022 (02:00 PM PDT - 03:00 PM PDT)
Speaker(s): Jeff Diller (University of Notre Dame)
Location: SLMath: Eisenbud Auditorium, Online/Virtual
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Invariant Currents For Surface Maps With Transcendental First Dynamical Degree

Abstract

Let f:X-->X be a rational map in complex dimension two. Assuming the first dynamical degree of f exceeds 1, there is a standard way to construct a dynamically natural positive closed current invariant under pullback. The construction requires, however, that f be `algebraically stable.' In this talk I'll focus on some recent examples where the dynamical degree is transcendental and construct invariant currents in a situation where algebraic stability is unachievable.

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93102?type=thumb Invariant Currents For Surface Maps With Transcendental First Dynamical Degree 217 KB application/pdf Download
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Invariant Currents For Surface Maps With Transcendental First Dynamical Degree

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