Logistic Map Potentials

Abstract

We develop and illustrate methods to compute all single particle potentials that underlie the logistic map, x --> sx(1-x) for 0<s<=4. We show that the switchback potentials can be obtained from the primary potential through functional transformations. We are thereby able to produce the various branches of the corresponding analytic potential functions, which have an infinite number of branch points for generic s>2. We illustrate the methods numerically for the cases s=5/2 and s=10/3.

References in corpus (3)

• Evolution profiles and functional equations
• Chaotic Maps, Hamiltonian Flows, and Holographic Methods
• Homoclinic Chaos in Axisymmetric Bianchi-IX cosmological models with an "ad hoc" quantum potential

Cited by in corpus (6)

• Renormalization Group Functional Equations
• Branched Hamiltonians and Supersymmetry
• Exploring Branched Hamiltonians for a Class of Nonlinear Systems
• Approximate Solutions of Functional Equations
• A reappraisal of Lagrangians with non-quadratic velocity dependence and branched Hamiltonians
• Potentials Unbounded Below