TL;DR
This paper provides a unified proof demonstrating turbulence in various classes of continuous interval maps, including those with certain periodic points and dense chaotic behavior.
Contribution
It offers a comprehensive proof establishing turbulence across multiple classes of interval maps, unifying previous scattered results.
Findings
Turbulence exists in maps with odd-periodic points > 1
Turbulence in maps with dense chain recurrent points
Turbulence in densely chaotic maps
Abstract
We give a unified proof of the existence of turbulence for some classes of continuous interval maps which include, among other things, maps with periodic points of odd periods > 1, some maps with dense chain recurrent points and densely chaotic maps.
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Taxonomy
TopicsMathematical Dynamics and Fractals · Stochastic processes and statistical mechanics · Theoretical and Computational Physics