Complex Dynamics in the Tropics - Deformations of One-Dimensional Maps - Lecture

Explore complex dynamics in the tropics through a 42-minute conference talk on deformations of one-dimensional maps. Delve into various types of one-dimensional maps, topological classes, smooth curves, and hybrid classes. Examine unique and continuous integrability, sigma functions, and checkable conditions. Investigate piecewise expanding maps, bounded functions, and linear continuous functions through examples. Analyze distributions, strong mixing, correlation, integration, and conjugacy. Discuss observatories, discontinuity, and preliminary results. This talk, presented by D. Smania at the Instituto de Matemática Pura e Aplicada, is part of an international congress celebrating Carsten Lunde Petersen's 60th birthday, uniting prominent researchers in the field to discuss the state of the art in complex dynamics.

Introduction
Types of onedimensional maps
Topological maps
Topological classes
Smooth curves
Hybrid classes
Unique integrability
Continuous integrability
Sigma functions
Checkable conditions
regularity
literature
piecewise expanding maps
a bounded function
a linear continuous function
examples
a distribution
strongly mixing
Correlation
Integration
Conjugacy
Observatories
Discontinuity
Next steps
Preliminary results