Renormalization for critical orders close to 2N

Judith Cruz; Daniel Smania

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arXiv · 1001.1271

Renormalization for critical orders close to 2N

Judith Cruz·Daniel Smania

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Abstract

We study the dynamics of the renormalization operator acting on the space of pairs (v,t), where v is a diffeomorphism and t belongs to [0,1], interpreted as unimodal maps x-->v(q_t(x)), where q_t(x)=-2t|x|^a+2t-1. We prove the so called complex bounds for sufficiently renormalizable pairs with bounded combinatorics. This allows us to show that if the critical exponent a is close to an even number then the renormalization operator has a unique fixed point. Furthermore this fixed point is hyperbolic and its codimension one stable manifold contains all infinitely renormalizable pairs.

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BibTeX RIS

Judith Cruz, Daniel Smania. 2010-01-08. Renormalization for critical orders close to 2N. https://arxiv.org/abs/1001.1271

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