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Discontinuity of Hausdorff dimension and limit capacity on arcs of diffeomorphisms

Published online by Cambridge University Press:  19 September 2008

Lorenzo J. Diaz  and
Marcelo Viana
Lorenzo J. Diaz
Affiliation:
IMPA, Estrada Dona Castorina 110, 22.460-Rio de Janeiro-RJ, Brasil
Marcelo Viana
Affiliation:
Departamento de Matemática, Fac. Ciências do Porto, 4000 Porto-Portugal
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Abstract

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We consider one-parameter families of torus diffeomorphisms that bifurcate from global hyperbolic maps (Anosov) to DA maps (derived from Anosov). For an open set of these families, we show that the Hausdorff dimension and limit capacity of the nonwandering set are not continuous across the bifurcation. We also study the behaviour of equilibrium measures near the bifurcation.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 9 , Issue 3 , September 1989 , pp. 403 - 425
Copyright
Copyright © Cambridge University Press 1989

References

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