Abstract
We present an infinite dimensional space of C 1 + smooth conjugacy classes of circle diffeomorphisms that are C 1 + fixed points of renormalization. We exhibit a one-to-one correspondence between these C 1 + fixed points of renormalization and C 1 + conjugacy classes of Anosov diffeomorphisms.
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Acknowledgements
Previous versions of this work were presented in the International Congresses of Mathematicians ICM 2006 and 2010, EURO 2010, ICDEA 2009 and in the celebration of David Rand’s 60th birthday, achievements and influence, University of Warwick. We are grateful to Dennis Sullivan and Flávio Ferreira for a number of very fruitful and useful discussions on this work and for their friendship and encouragement. We thank LIAAD-INESC Porto LA, Calouste Gulbenkian Foundation, PRODYN-ESF, POCTI and POSI by FCT and Ministério da Ciência e da Tecnologia, and the FCT Pluriannual Funding Program of the LIAAD-INESC Porto LA and of the Research Centre of Mathematics of University of Minho, for their financial support. A. Fisher would like to thank FAPESP, the CNPQ and the CNRS for their financial support.
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Almeida, J.P., Fisher, A.M., Pinto, A.A., Rand, D.A. (2011). Anosov and Circle Diffeomorphisms. In: Peixoto, M., Pinto, A., Rand, D. (eds) Dynamics, Games and Science I. Springer Proceedings in Mathematics, vol 1. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-11456-4_2
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DOI: https://doi.org/10.1007/978-3-642-11456-4_2
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