Moduli of stability of two-dimensional diffeomorphisms (original) (raw)

This paper investigates diffeomorphisms on compact two-dimensional manifolds characterized by a pair of hyperbolic periodic points with a specific tangency relationship between their stable and unstable manifolds. The central focus is on the concept of modulus of stability, which quantifies the number of parameters needed to describe topological equivalence classes around a diffeomorphism. Results show that under particular conditions, the modulus of stability can be finite or infinite. Furthermore, the study considers G-equivariant diffeomorphisms where the action of a finite group induces a structural persistence of tangency phenomena, leading to the possibility of parametrizing stability classes with finitely many parameters.