Critical set for surface diffeomorphisms revisited

TL;DR

This paper introduces a new concept of critical sets for surface diffeomorphisms, aiming to extend the role of critical points from one-dimensional dynamics to two-dimensional cases.

Contribution

It defines an intrinsic notion of critical sets for surface diffeomorphisms, providing a foundation for analyzing complex surface dynamics.

Findings

Defines a new critical set concept for surface diffeomorphisms

Establishes the role of critical sets analogous to critical points in 1D dynamics

Provides a framework for future dynamical analysis on surfaces

Abstract

We propose a notion of critical set for two-dimensional surface diffeomorphisms as an intrinsically defined object designed to play a role analogous to that of critical points in one-dimensional dynamics.