Symmetry of Lyapunov exponents in bifurcation structures of one-dimensional maps

摘要

We observe a symmetry of Lyapunov exponents in bifurcation structures of one-dimensional maps in which there exists a pair of parameter values in a dynamical system such that two dynamical systems with these paired parameter values have the same Lyapunov exponent. We show that this is a consequence of the presence of an invariant transformation from a dynamical system with one of the two paired parameter values to that with another parameter value, which does not change natures of dynamical systems. (C) 2016 Author(s).