Local study of  a renormalization operator for 1D maps under  quasiperiodic forcing

Àngel Jorba; Pau  Rabassa; Joan Carles  Tatjer

doi:10.3934/dcdss.2016047

Article Contents

2016, Volume 9, Issue 4: 1171-1188. Doi: 10.3934/dcdss.2016047

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Local study of a renormalization operator for 1D maps under quasiperiodic forcing

1.
Departament de Matemàtica Aplicada i Anàlisi, Universitat de Barcelona, Gran Via 585 , 08007 Barcelona
2.
School of Mathematical Sciences, Queen Mary University of London, Mile End Road, London E1 4NS
3.
Departament de Matemàtiques i Informàtica, Universitat de Barcelona, Gran Via 585, 08007 Barcelona

Received: August 31, 2015

Revised: November 30, 2015

Published: July 2016

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Abstract

The authors have recently introduced an extension of the classical one dimensional (doubling) renormalization operator to the case where the one dimensional map is forced quasiperiodically. In the classic case the dynamics around the fixed point of the operator is key for understanding the bifurcations of one parameter families of one dimensional unimodal maps. Here we perform a similar study of the (linearised) dynamics around the fixed point for further application to quasiperiodically forced unimodal maps.

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Mathematics Subject Classification: Primary: 37C55; Secondary: 37E20, 37G35.

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