A Bernoulli toral linked twist map

without positive Lyapunov exponents

Author:
Matthew Nicol

Journal:
Proc. Amer. Math. Soc. **124** (1996), 1253-1263

MSC (1991):
Primary 58F11; Secondary 58F15

MathSciNet review:
1327031

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Abstract | References | Similar Articles | Additional Information

Abstract: The presence of positive Lyapunov exponents in a dynamical system is often taken to be equivalent to the chaotic behavior of that system. We construct a Bernoulli toral linked twist map which has positive Lyapunov exponents and local stable and unstable manifolds defined only on a set of measure zero. This is a deterministic dynamical system with the strongest stochastic property, yet it has positive Lyapunov exponents only on a set of measure zero. In fact we show that for any map in a certain class of piecewise linear Bernoulli toral linked twist maps, given any there is a Bernoulli toral linked twist map with positive Lyapunov exponents defined only on a set of measure zero such that is within of in the metric.

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Additional Information

**Matthew Nicol**

Affiliation:
Department of Mathematics, University of Houston, Houston, Texas 77204-3476 \indent{E-mail address}: nicol@math.uh.edu

Address at time of publication:
Department of Mathematics, UMIST, PO Box 88, Manchester M60 1QD, United Kingdom

Email:
nicol@math.uh.edu, matt@maths.warwick.ac.uk

DOI:
http://dx.doi.org/10.1090/S0002-9939-96-03357-6

Keywords:
Lyapunov exponent,
linked twist map

Received by editor(s):
June 2, 1994

Communicated by:
Linda Keen

Article copyright:
© Copyright 1996
American Mathematical Society