Families of piecewise linear maps with constant Lyapunov exponent
V. Botella-Soler, J. A. Oteo, J. Ros, P. Glendinning

TL;DR
This paper investigates families of piecewise linear maps with varying slopes, demonstrating that in certain parameter regions, the Lyapunov exponent and topological entropy remain constant, supported by numerical and analytical evidence.
Contribution
It introduces new families of maps with constant Lyapunov exponents across parameter regions and provides both numerical and analytical validation of this phenomenon.
Findings
Lyapunov exponent remains constant in certain parameter regions
Topological entropy is also constant in these regions
The mechanism differs from logistic map dynamics
Abstract
We consider families of piecewise linear maps in which the moduli of the two slopes take different values. In some parameter regions, despite the variations in the dynamics, the Lyapunov exponent and the topological entropy remain constant. We provide numerical evidence of this fact and we prove it analytically for some special cases. The mechanism is very different from that of the logistic map and we conjecture that the Lyapunov plateaus reflect arithmetic relations between the slopes.
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Taxonomy
TopicsMathematical Dynamics and Fractals · Chaos control and synchronization · Quantum chaos and dynamical systems
