# American Institute of Mathematical Sciences

August  2016, 9(4): 1171-1188. doi: 10.3934/dcdss.2016047

## 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, United Kingdom 3 Departament de Matemàtiques i Informàtica, Universitat de Barcelona, Gran Via 585, 08007 Barcelona, Spain

Received  September 2015 Revised  December 2015 Published  August 2016

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.
Citation: Àngel Jorba, Pau Rabassa, Joan Carles Tatjer. Local study of a renormalization operator for 1D maps under quasiperiodic forcing. Discrete & Continuous Dynamical Systems - S, 2016, 9 (4) : 1171-1188. doi: 10.3934/dcdss.2016047
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