Fibred quadratic polynomials can admit two attracting invariant curves
Abstract: We present an example of a fibred quadratic polynomial admitting two attracting invariant curves. This phenomena cannot occur in the non-fibred setting.
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- Lennart Carleson and Theodore W. Gamelin.
Universitext: Tracts in Mathematics. Springer-Verlag, New York, 1993. MR 1230383 (94h:30033)
- Mario Ponce.
Local dynamics for fibred holomorphic transformations.
Nonlinearity, 20(12):2939-2955, 2007. MR 2368333 (2009b:37090)
- Olivier Sester.
Hyperbolicité des polynômes fibrés.
Bull. Soc. Math. France, 127(3):393-428, 1999. MR 1724402 (2000j:37057)
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Affiliation: Department of Mathematics, Pontifical Catholic University, Vicuna Mackenna Avenue, 4860 Santiago, Chile
Received by editor(s): November 19, 2009
Received by editor(s) in revised form: March 19, 2010, April 9, 2010, April 29, 2010, and May 5, 2010
Published electronically: October 5, 2010
Additional Notes: This research was partially supported by FONDECYT 11090003.
Communicated by: Bryna Kra
Article copyright: © Copyright 2010 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.