Abstract
Existence of an invariant circle for any orientation-preserving 2D map whose orbit under renormalisation remains forever in a certain bounded subset is proved. The construction dates back to 1984. It was stimulated by a preprint by David Rand doing the same for the dissipative case. To include the general case, notably area-preserving, required a variation on his idea.
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References
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Acknowledgements
I am grateful to David Rand for the interest he has always shown in my work and for the stimulation he has provided to me. And I thank Elaine Greaves-Coelho for preparing the figures for me.
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© 2011 Springer-Verlag Berlin Heidelberg
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MacKay, R.S. (2011). Existence of Invariant Circles for Infinitely Renormalisable Area-Preserving Maps. 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_39
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DOI: https://doi.org/10.1007/978-3-642-11456-4_39
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