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Explore the intricacies of interval map dynamics in this 1 hour 20 minute lecture by Genadi Levin from the Hebrew University of Jerusalem. Delve into the monotonicity of entropy in families of interval maps, transfer operators, and holomorphic motions. Examine the Ruelle-Thurston transfer operator and its applications in rational dynamics. Analyze an explicit example involving disconnected quadratic Julia sets and the limit distribution of eigenvalues. Compare Tsujii's and Milnor-Thurston's approaches to entropy monotonicity in the real quadratic family. Investigate a local approach using holomorphic motions, focusing on the transfer operator and its spectrum. Discover the main theorem and its applications, and explore the critically infinite case, questioning whether saddle-nodes unfold in a positive direction. This lecture, part of the Simons Semester on Dynamics, offers a comprehensive exploration of advanced concepts in dynamical systems theory.
