Chaotic self-similar wave maps coupled to gravity
Sebastian J. Szybka
TL;DR
This paper investigates chaotic self-similar solutions in the SU(2) sigma model coupled to gravity, revealing fractal threshold behavior and complex dynamics through numerical and theoretical analysis.
Contribution
It provides the first numerical evidence of chaos and fractal thresholds in self-similar solutions of the SU(2) sigma model coupled to gravity, explaining the phenomena via horseshoe dynamics.
Findings
Chaotic solutions observed for certain coupling constants.
Fractal threshold behavior identified in the solution space.
Horseshoe-like dynamics and heteroclinic intersections explain chaos.
Abstract
We continue our studies of spherically symmetric self-similar solutions in the SU(2) sigma model coupled to gravity. For some values of the coupling constant we present numerical evidence for the chaotic solution and the fractal threshold behavior. We explain this phenomenon in terms of horseshoe-like dynamics and heteroclinic intersections.
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