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Article

Renormalization for Lorenz maps of monotone combinatorial types

  • DENIS GAIDASHEV (a1)

Abstract

Lorenz maps are maps of the unit interval with one critical point of order $\unicode[STIX]{x1D70C}>1$ and a discontinuity at that point. They appear as return maps of sections of the geometric Lorenz flow. We construct real a priori bounds for renormalizable Lorenz maps with certain monotone combinatorics and a sufficiently flat critical point, and use these bounds to show existence of periodic points of renormalization, as well as existence of Cantor attractors for dynamics of infinitely renormalizable Lorenz maps.

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© Cambridge University Press, 2017 

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Renormalization for Lorenz maps of monotone combinatorial types

  • DENIS GAIDASHEV (a1)

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