Wandering Intervals for Lorenz Maps with Bounded Nonlinearity

1991/03/01 by D. Berry, David Berry, B. D. Mestel +1 · 1 citation
Mathematics · Physics and Astronomy · #Mathematical Dynamics and Fractals #Chaos control and synchronization #Advanced Differential Equations and Dynamical Systems

paper · doi:10.1112/blms/23.2.183

Abstract

A Lorenz map satisfying a bounded nonlinearity condition is shown not to admit wandering intervals unless it renormalises to a non-surjective circle map (gap map) with irrational rotation number.

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• The boundary of chaos for piecewise smooth maps and the boundary of positive Hausdorff dimension for survivor sets of open maps

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