Braid Equivalence in the H\'enon Family I
Andr\'e de Carvalho, Toby Hall, Peter Hazard
TL;DR
This paper introduces two general methods for constructing braid equivalences in deformations of the 2-branched Horseshoe map and provides numerical evidence that these equivalences occur in the Hénon family.
Contribution
It presents new constructions of braid equivalences and suggests their universal realization in the Hénon family through numerical analysis.
Findings
Two general constructions of braid equivalences for deformations of the 2-branched Horseshoe map.
Numerical evidence indicating these braid equivalences are realized in the Hénon family.
Potential universality of the braid equivalences in the Hénon family.
Abstract
We give two general constructions of braid equivalences which exist between certain deformations of the 2-branched Horsehoe map. We then give numerical evidence suggesting that these constructions of braid equivalences are always realised in the H\'enon family.
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Taxonomy
TopicsHomotopy and Cohomology in Algebraic Topology · Geometric and Algebraic Topology · Algebraic Geometry and Number Theory