Symmetry of Lyapunov exponents in bifurcation structures of one-dimensional maps. (English) Zbl 1378.37030
Summary: 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.{
©2016 American Institute of Physics}
©2016 American Institute of Physics}
MSC:
| 37B25 | Stability of topological dynamical systems |
Software:
Symmetry in ChaosReferences:
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