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London Mathematical Society, Bulletin of the London Mathematical Society, 3(34), p. 341-352, 2002

DOI: 10.1112/s0024609301008670

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Smoothness of holonomies for codimension 1 hyperbolic dynamics

Journal article published in 2002 by Pinto Aa, A. A. Pinto, D. A. (David A.) Rand, D. A. (David A.) Rand ORCID
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Abstract

Hyperbolic invariant sets Λ of C1+γ diffeomorphisms where either the stable or unstable leaves are 1-dimensional are considered in this paper. Under the assumption that the Λ has local product structure, the authors prove that the holonomies between the 1-dimensional leaves are C1+α for some 0 < α < 1.