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Hyperbolic cantori have dimension zero

R S MacKay

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It is proved that cantori for area-preserving twist maps have dimension zero, only finitely many orbits of gaps, and gap widths go to zero exponentially in each orbit, if they are hyperbolic.


PACS

05.45.-a Nonlinear dynamics and nonlinear dynamical systems

05.20.-y Classical statistical mechanics

MSC

37E40 Twist maps

37D05 Hyperbolic orbits and sets

37A35 Entropy and other invariants, isomorphism, classification

Subjects

Statistical physics and nonlinear systems

Dates

Issue 9 (21 June 1987)



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