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A hyperelliptic realization of the horseshoe and baker maps

Published online by Cambridge University Press:  01 November 2006

R. CHAMANARA ,
F. P. GARDINER  and
N. LAKIC
R. CHAMANARA
Affiliation:
Department of Mathematics, Indiana University, Bloomington, IN 47405, USA (e-mail: rchamana@indiana.edu)
F. P. GARDINER
Affiliation:
Department of Mathematics, Brooklyn College, Brooklyn, NY 11210, USA (e-mail: fgardiner@gc.cuny.edu)
N. LAKIC
Affiliation:
Department of Mathematics, Herbert H. Lehman College, Bronx, NY 10468, USA (e-mail: nlakic@lehman.cuny.edu)
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Abstract

We present a generalization of the functional equation for the Weierstrassk $\wp$-function for hyperelliptic surfaces of infinite genus arising from iteration of the horseshoe and baker maps. The ramified cover of these infinite genus surfaces over the complex plane are associated to a quadratic differential of finite norm with simple poles accumulating to infinity. We study the geometry of its critical trajectories emanating from these poles and their rate of accumulation.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 26 , Issue 6 , December 2006 , pp. 1749 - 1768
Copyright
2006 Cambridge University Press

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