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                                       Details for article 5 of 8 found articles
  On the volume of singular-hyperbolic sets
Title: On the volume of singular-hyperbolic sets
Author: Alves, J. F.
Araujo, V.
Pacifico, M. J.
Pinheiro, V.
Appeared in: Dynamical systems
Paging: Volume 22 (2007) nr. 3 pages 249-267
Year: 2007-09
Contents: An attractor Λ for a 3-vector field X is singular-hyperbolic if all its singularities are hyperbolic and it is partially hyperbolic with volume expanding central direction. We prove that C1 + α singular-hyperbolic attractors, for any α > 0, always have zero volume, extending an analogous result for uniformly hyperbolic attractors. The same result holds for a class of higher dimensional singular attractors. Moreover, we prove that if Λ is a singular-hyperbolic attractor for X then either it has zero volume or X is an Anosov flow. We also present examples of C1 singular-hyperbolic attractors with positive volume. In addition, we show that C1 generically we have volume zero for C1 robust classes of singular-hyperbolic attractors.
Publisher: Taylor & Francis
Source file: Elektronische Wetenschappelijke Tijdschriften

                             Details for article 5 of 8 found articles
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