Fibred quadratic polynomials can admit two attracting invariant curves
HTML articles powered by AMS MathViewer
- by Mario Ponce PDF
- Proc. Amer. Math. Soc. 139 (2011), 1467-1468 Request permission
Abstract:
We present an example of a fibred quadratic polynomial admitting two attracting invariant curves. This phenomena cannot occur in the non-fibred setting.References
- Lennart Carleson and Theodore W. Gamelin, Complex dynamics, Universitext: Tracts in Mathematics, Springer-Verlag, New York, 1993. MR 1230383, DOI 10.1007/978-1-4612-4364-9
- Mario Ponce, Local dynamics for fibred holomorphic transformations, Nonlinearity 20 (2007), no. 12, 2939–2955. MR 2368333, DOI 10.1088/0951-7715/20/12/011
- Olivier Sester, Hyperbolicité des polynômes fibrés, Bull. Soc. Math. France 127 (1999), no. 3, 393–428 (French, with English and French summaries). MR 1724402
Additional Information
- Mario Ponce
- Affiliation: Department of Mathematics, Pontifical Catholic University, Vicuna Mackenna Avenue, 4860 Santiago, Chile
- Email: mponcea@mat.puc.cl
- 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
- © Copyright 2010
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc. 139 (2011), 1467-1468
- MSC (2010): Primary 37F10
- DOI: https://doi.org/10.1090/S0002-9939-2010-10574-9
- MathSciNet review: 2748440