On a generalization of the logistic map
Valerie Poulin, Hugo Touchette
Abstract
A family of non-conjugate chaotic maps generalizing the well-known logistic function is defined, and some of its basic properties studied. A simple formula for the Lyapunov exponents of all the maps contained in this family is given based on the construction of conjugacies. Moreover, it is shown that, despite the dissimilarity of their polynomial expressions, all the maps possess the same invariant density. Other algebraic properties of the family, which shows some relationship with the set of Tschebysheff polynomials, are also investigated.
Create a lesson
Related papers
Ordinal-pattern transition networks as a symbolic substrate for reservoir computing
Max Potratzki, Thomas G. de Jong, Michael Small et al.
A general feedback mechanism unifying stochasticity, long transients, and resilience
Misha Chai, Holger Kantz
Statistical Characterization of Erratic and Chaotic Processes through Their Extrema I. Thermodynamics
Jacob Sonnenschein
Online training of Echo State Networks to predict chaotic dynamical systems
Astero Provata, Markos Syroukis, Johanne Hizanidis
Partial Multistep Prediction of Chaotic Time Series: What Remains Predictable beyond the Horizon of Predictability?
Vasilii A. Gromov, Maksim Lomakin, Aleksei Kudryashov et al.
Stability of inverse cascade in NLS Wave turbulence
Guillaume Costa, Sergey Nazarenko, Giorgio Krstulovic