Algebraic, Complex, and Arithmetic Dynamics

This book grew out of a series of three Simons Symposia in 2019, 2022, and 2024, that focused on the interactions between three types of dynamics—algebraic, complex, and arithmetic—and their connections to the closely related areas of algebraic, complex, and arithmetic geometry. Dynamical systems play a key role both in pure mathematics and its applications. These meetings brought experts together from across these fields for discussions on the most significant recent developments and directions for further research.

Preface.- Dynamical Degrees, Arithmetic Degrees, and Canonical Heights: History, Conjectures, and Future Direction.- Recent Advances on Kawaguchi-Silverman Conjecture.- Around the Dynamical Mordell-Lang Conjecture.- Advances in the Equivariant Minimal Model Program and their Applications in Complex and Arithmetic Dynamics.- Dynamics of Automorphism Groups of Projective Surfaces: Classification, Examples and Outlook.- Questions About the Dynamics on a Natural Family of Affine Cubic Surfaces.- Holomorphic Motions of Weighted Periodic Points.- On Slice Measures of Green Currents on CP2.- Hölder Estimates and Uniformity in Arithmetic Dynamics.- Entire or Rational Maps with Integer Multipliers.- Tischler Graphs of Critically Fixed Rational Maps and their Applications.- Mirrors of Conformal Dynamics: Interplay Between Anti-Rational Maps, Reflection Groups, Schwarz Reflections, and Correspondences.- On Boundedness of Zeroes of the Independence Polynomial of Tori.