Contracting singular horseshoe

We suggest a notion of hyperbolicity adapted to the geometric Rovella attractor (Robinson 2012 An Introduction to Dynamical Systems-Continuous and Discrete (Pure and Applied Undergraduate Texts vol 19) 2nd edn (Providence, RI: American Mathematical Society)) . More precisely, we call a partially hyp...

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Bibliographic Details
Published in:Nonlinearity 2017-11, Vol.30 (11), p.4208-4219
Main Authors: Morales, C A, San Martín, B
Format: Article
Language:English
Subjects:
asymptotically sectional-hyperbolic
flow
sectional-hyperbolic
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Summary:We suggest a notion of hyperbolicity adapted to the geometric Rovella attractor (Robinson 2012 An Introduction to Dynamical Systems-Continuous and Discrete (Pure and Applied Undergraduate Texts vol 19) 2nd edn (Providence, RI: American Mathematical Society)) . More precisely, we call a partially hyperbolic set asymptotically sectional-hyperbolic if its singularities are hyperbolic and if its central subbundle is asymptotically sectional expanding outside the stable manifolds of the singularities. We prove that there are highly chaotic flows with Rovella-like singularities exhibiting this kind of hyperbolicity. We shall call them contracting singular horseshoes.
ISSN:0951-7715
1361-6544
DOI:10.1088/1361-6544/aa864e