Renormalization and conjugacy of piecewise linear Lorenz maps

2009/06/17 by Hongfei Cui, Yiming Ding, Cui, Hong-Fei +1 · 2 citations
Mathematics · Computer Science · #Mathematical Dynamics and Fractals #Advanced Differential Equations and Dynamical Systems #Nonlinear Dynamics and Pattern Formation

paper · pdf · doi:10.48550/arxiv.0906.3131

Abstract

For each piecewise linear Lorenz map that expand on average, we show that it admits a dichotomy: it is either periodic renormalizable or prime. As a result, such a map is conjugate to a β-transformation.

Cited by

• Kneading the Lorenz attractor
• Absolutely Continuous Invariant Measures of Piecewise Linear Lorenz Maps

Related

• Renormalization and alpha-limit set for expanding Lorenz maps
• Complete invariants and parametrization of expansive Lorenz maps
• Renormalization for Lorenz maps of monotone combinatorial types
• A piecewise linear homeomorphism of the circle which is periodic under renormalization
• Forcing of periodic orbits for interval maps and renormalization of piecewise affine maps