Sufficient conditions for a period incrementing big bang bifurcation in one-dimensional maps

Abstract

\n Typically, big bang bifurcation occur for one (or\n higher)-dimensional piecewise-defined systems whenever two border\n collision bifurcation curves collide transversely in the parameter\n space. At that point, two (feasible) fixed points collide with the\n boundary in state space and become virtual. Depending on the\n properties of the map near the codimension-two bifurcation point,\n there exist different scenarios regarding how the infinite number of\n periodic orbits are born, mainly the so-called period adding and\n period incrementing. In our work we prove that, in order to undergo\n a big bang bifurcation of the period incrementing type, it is\n sufficient for a piecewise-defined one-dimensional map that the\n colliding fixed points are attractive and with associated\n eigenvalues of different sign\n