On Kolmogorov-typical properties of symplectic dynamics

TL;DR

This paper introduces a framework demonstrating that key dynamical properties like periodic point growth and universality are generically present in symplectic diffeomorphisms with elliptic points across parameter spaces.

Contribution

It provides a general framework proving that several complex dynamical properties are typical in a broad class of symplectic systems with elliptic points.

Findings

Fast growth of periodic points

Universality in symplectic dynamics

High emergence across parameters

Abstract

We propose a general framework, within which we prove that several properties, such as the fast growth of the number of periodic points, the universality, and the high emergence, hold true for every parameter value for a generic finite-parameter family of symplectic diffeomorphisms displaying an elliptic point.