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Monotonicity of Entropy in Families of Interval Maps - Lecture 1

Simons Semester on Dynamics via YouTube

Overview

Explore the intricacies of interval map dynamics in this comprehensive lecture on monotonicity of entropy, transfer operators, and holomorphic motions. Delve into the Ruelle-Thurston transfer operator and examine an explicit example involving disconnected quadratic Julia sets and eigenvalue limit distributions. Investigate applications to rational dynamics and compare Tsujii's and Milnor-Thurston's approaches to entropy monotonicity in the real quadratic family. Analyze a local approach using holomorphic motions, focusing on the transfer operator and its spectrum. Discover the main theorem and its applications, and consider the critically infinite case, questioning whether saddle-nodes unfold in a positive direction.

Syllabus

Genadi Levin (Hebrew University of Jerusalem) lecture 1

Taught by

Simons Semester on Dynamics

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