title: Symmetry of Lyapunov exponents in bifurcation structures of one-dimensional maps.
abstract: 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.
authors.affiliation: Department of Information and Computer Technology, Faculty of Engineering, Tokyo University of Science, 6-3-1 Niijuku, Katsushika-ku, Tokyo 125-8585, Japan.
authors.forename: Yutaka
authors.initials: Y
authors.lastname: Shimada
authors.affiliation: Department of Management Science, Faculty of Engineering Division II, Tokyo University of Science, 6-3-1 Niijuku, Katsushika-ku, Tokyo 125-8585, Japan.
authors.forename: Emiko
authors.initials: E
authors.lastname: Takagi
authors.affiliation: Department of Information and Computer Technology, Faculty of Engineering, Tokyo University of Science, 6-3-1 Niijuku, Katsushika-ku, Tokyo 125-8585, Japan.
authors.forename: Tohru
authors.initials: T
authors.lastname: Ikeguchi