Sectional Curvature and Chaos in Dynamical Problems: Toward the Invariant Measure of Chaos in Hamiltonian Systems

Abstract

Chaotic phenomena in general relativity are investigated. In relativistic astrophysical problems no space-time coordinate system is privileged in any way as far as the physical description of phenomena is concerned. Effects which depend on the choice of the particular coordinate system should be treated as an artifact of the incorrect methods. To avoid such difficulties the gauge invariant theory of chaos is proposed.