Renormalization for Lorenz maps of long monotone combinatorial types

Details Renormalization for Lorenz maps of long monotone combinatorial types Renormalization for Lorenz maps of long monotone combinatorial types

2012-04-11

arxiv.org/abs/1204.2504v2

Mathematics

Dynamical Systems

Scientific paper

Lorenz maps are maps of the unit interval with one critical point of order rho>1, and a discontinuity at that point. They appear as return maps of leafs of sections of the geometric Lorenz flow. We construct real a priori bounds for renormalizable Lorenz maps with long monotone combinatorics, 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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