Chaotic self-similar wave maps coupled to gravity

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.

25 pages, 17 figures

References in corpus (3)

• Critical phenomena in gravitational collapse (Physics Reports)
• On the existence of self-similar spherically symmetric wave maps coupled to gravity
• Periodic self-similar wave maps coupled to gravity

Cited by in corpus (5)

• Periodic self-similar wave maps coupled to gravity
• Fractal Threshold Behavior in Vacuum Gravitational Collapse
• Analytical solutions for black-hole critical behaviour
• Bifurcation and fine structure phenomena in critical collapse of a self-gravitating $\sigma$-field
• Spectral Properties and Stability of Self-Similar Wave Maps