Examples on Perron effects in autonomous discrete systems

Abstract

We construct examples proving that there exist C1-dynamical systems in [0,1) having forward orbits instable in the sense of Lyapunov with negative Lyapunov exponent and forward orbits stable in the same sense, but having positive Lyapunov exponents. Such examples complete some results from Demir and Koçak for one dimensional systems and prove the appearance of Perron effects in such systems. Additionally we consider similar problems in two dimensional dynamical systems.