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The shear-rotation interval of twist maps

Published online by Cambridge University Press:  09 January 2002

SINIšA SLIJEPČEVIĆ
SINIšA SLIJEPČEVIĆ
Affiliation:
Department of Mathematics, Bijenička 30, 10000 Zagreb, Croatia (e-mail: [email protected])
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Abstract

Given a twist map on the torus, we prove that the non-existence of a rotational invariant circle implies that the shear-rotation interval is non-trivial, i.e. the existence of orbits with non-zero mean acceleration. Under the same assumption, we prove the existence of infinitely many periodic orbits and positive entropy invariant measures with non-zero shear-rotation number. The method is variational, but relies on topological understanding of the shear-rotation interval of torus homeomorphisms homotopic to a Dehn twist.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 22 , Issue 1 , February 2002 , pp. 303 - 313
Copyright
2002 Cambridge University Press

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