Journal of Mathematics of Kyoto University

A partial horseshoe structure at an indeterminate point of birational mapping

Tomoko Shinohara

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Abstract

In this paper, we show that, for some birational mapping $F$ of $\mathbb{P} ^{2}$ with an indeterminate point $I_{1}$, there exists a partial horseshoe structure at $I_{1}$ and periodic points of $F$ accumulate at $I_{1}$. This is a new dynamical model that gives a chaotic phenomenon in a neighbourhood of the indeterminate point $I_{1}$ at which $F$ is not continuous.

Article information

Source
J. Math. Kyoto Univ., Volume 47, Number 1 (2007), 15-33.

Dates
First available in Project Euclid: 14 August 2009

Permanent link to this document
https://projecteuclid.org/euclid.kjm/1250281066

Digital Object Identifier
doi:10.1215/kjm/1250281066

Mathematical Reviews number (MathSciNet)
MR2359099

Zentralblatt MATH identifier
1144.37019

Subjects
Primary: 32H50: Iteration problems
Secondary: 37F10: Polynomials; rational maps; entire and meromorphic functions [See also 32A10, 32A20, 32H02, 32H04]

Citation

Shinohara, Tomoko. A partial horseshoe structure at an indeterminate point of birational mapping. J. Math. Kyoto Univ. 47 (2007), no. 1, 15--33. doi:10.1215/kjm/1250281066. https://projecteuclid.org/euclid.kjm/1250281066


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