The creation of horseshoes
- 1 May 1994
- journal article
- Published by IOP Publishing in Nonlinearity
- Vol. 7 (3) , 861-924
- https://doi.org/10.1088/0951-7715/7/3/008
Abstract
We present results which describe constraints on the order in which periodic orbits can appear when a horseshoe is created. We associate two rational numbers q(R) and r(R) to each periodic orbit R of the horseshoe, which have the property that if r(R)<q(S) then the orbit R must appear after the orbit S; while if r(S)<r(R) and q(R)<q(S) then either orbit can appear before the other. The time required to compute these quantities is bounded by a linear function of the period of R. We also present an algorithm for determining the rotation interval of a horseshoe orbit, and describe techniques for obtaining lower bounds on the topological entropy of a horseshoe orbit.Keywords
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