Moduli of surface diffeomorphisms with cubic tangencies
Shinobu Hashimoto
TL;DR
This paper investigates conjugacy invariants for 2D surface diffeomorphisms with homoclinic cubic tangencies, introducing a novel method to handle the complexities of two-sided tangencies which differ from previous one-sided cases.
Contribution
It develops a new approach for analyzing conjugacy invariants in the challenging context of two-sided homoclinic cubic tangencies.
Findings
Introduces a new method for two-sided tangencies
Establishes conjugacy invariants under certain conditions
Addresses limitations of previous one-sided tangency techniques
Abstract
In this paper, we study conjugacy invariants for 2-dimensional diffeomorphisms with homoclinic cubic tangencies (two-sided tangencies of the lowest order) under certain open conditions. Ordinary arguments used in past studies of conjugacy invariants associated with one-sided tangencies do not work in the two-sided case. We present a new method which is applicable to the two-sided case.
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