Order and chaos in hydrodynamic BL Her models

Abstract

Many dynamical systems of different complexity, e.g. 1D logistic map, the Lorentz equations, or real phenomena, like turbulent convection, show chaotic behaviour. Despite huge differences, the dynamical scenarios for these systems are strikingly similar: chaotic bands are born through the series of period doubling bifurcations and merge through interior crises. Within chaotic bands periodic windows are born through the tangent bifurcations, preceded by the intermittent behaviour. This is a universal behaviour of dynamical systems (Feigenbaum 1983). We demonstrate such behaviour in models of pulsating stars.

2 pages, 1 figure, to appear in the conference proceedings of IAU Symp. 301 "Precision Asteroseismology, Celebration of the Scientific Opus of Wojtek Dziembowski", Wroclaw, Poland, August 2013