Program
![Image](/system/paperclip/programs/data/000/085/940/original/image.png)
The mating of these two dendritic Julia sets is equal to the Julia set of a rational map of degree 2; that Julia set is equal to the entire Riemann sphere. Picture by Arnaud Chéritat
Holomorphic dynamics is a vibrant field of mathematics that has seen profound progress over the past 40 years. It has numerous interconnections to other fields of mathematics and beyond.
Our semester will focus on three selected classes of dynamical systems: rational maps (postcritically finite and beyond); transcendental maps; and maps in several complex variables. We will put particular emphasis on the interactions between each these, and on connections with adjacent areas of mathematics.
Bibliography
Keywords and Mathematics Subject Classification (MSC)
Tags/Keywords
Holomorphic dynamics
iteration
Fatou set
Julia set
Mandelbrot set
renormalization
parameter spaces
postcritically finite maps
iterated monodromy groups
Thurston theory
arithmetic dynamics
transcendental dynamics
quasiconformal folding
Several Complex Variables
wandering domains
30Dxx - Entire and meromorphic functions of one complex variable, and related topics
37Fxx - Dynamical systems over complex numbers [See also 30D05, 32H50]
37Gxx - Local and nonlocal bifurcation theory for dynamical systems [See also 34C23, 34K18]
37Hxx - Random dynamical systems [See also 15B52, 34Fxx, 47B80, 70L05, 82C05, 93Exx]
37Pxx - Arithmetic and non-Archimedean dynamical systems [See also 11S82, 37A44]
February 02, 2022 - February 04, 2022 | [HYBRID WORKSHOP] Connections Workshop: Complex Dynamics - from special families to natural generalizations in one and several variables |
February 08, 2022 - February 17, 2022 | [HYBRID WORKSHOP] Introductory Workshop: Complex Dynamics - from special families to natural generalizations in one and several variables |
May 02, 2022 - May 06, 2022 | Adventurous Berkeley Complex Dynamics |