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A property of compact, connected, laminated subsets of manifolds

Published online by Cambridge University Press:  02 October 2002

JOHN N. MATHER
JOHN N. MATHER
Affiliation:
Department of Mathematics, Princeton University, Princeton, NJ 08544, USA (e-mail: [email protected])
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Abstract

Let X be a compact, connected subset of a smooth manifold. Suppose that X admits a codimension d lamination, d\ge 2. Let x,y\in X and \epsilon>0. There exists a sequence x=x_0,\dotsc,x_k=y in X such that the sum of the dth powers of the distances between successive points is less than \epsilon. We discuss two proposed applications of this result.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 22 , Issue 5 , October 2002 , pp. 1507 - 1520
Copyright
© 2002 Cambridge University Press

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