Infinitesimal Deformations: One-Dimensional Maps

This lecture by the instructor covers the study of infinitesimal deformations of one-dimensional maps, focusing on various types of dynamical systems such as piecewise expanding maps, unimodal maps, multimodal maps, diffeomorphisms of the circle, and more. The lecture explores the common characteristics shared by these systems, the methods to deform maps, and the implications on dynamics. It presents a general method to demonstrate that the topological class is a finite codimension smooth manifold, discussing assumptions, derivations, and conclusions. The lecture also delves into theorems and recent results related to expanding and piecewise expanding maps, including regularity, uniqueness of solutions, and applications of Ergodic Theory.