2015
DOI: 10.1088/0951-7715/28/6/1695
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Abstract: Let M be a surface and R : M → M an involution whose set of fixed points is a submanifold with dimension 1 and such that DR x ∈ SL(2, R) for all x. We will show that there is a residual subset of C 1 areapreserving R-reversible diffeomorphisms which are either Anosov or have zero Lyapunov exponents at almost every point.

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Cited by 5 publications
(14 citation statements)
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References 55 publications
(105 reference statements)
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“…We refer the reader to the survey [1] that consider numerous kinds of closing lemmas. Using similar arguments to those of [25] combined with [4], we state and prove the following version of the C 1 -Closing Lemma: Theorem A (The Reversible C 1 -Closing Lemma). Let R be an isometric involution on M .…”
Section: Statement Of the Main Resultsmentioning
confidence: 99%
See 4 more Smart Citations
“…We refer the reader to the survey [1] that consider numerous kinds of closing lemmas. Using similar arguments to those of [25] combined with [4], we state and prove the following version of the C 1 -Closing Lemma: Theorem A (The Reversible C 1 -Closing Lemma). Let R be an isometric involution on M .…”
Section: Statement Of the Main Resultsmentioning
confidence: 99%
“…Since there is a gap in the classic literature concerning the reversible systems, in the present paper we revisit the construction of perturbation toolboxes, namely local perturbations lemmas [4] and the Frankstype lemma [4] in Section 3, after having provided some preliminaries and notation in Section 2. The proof of Theorem A is done is Section 4 and those of Proposition 1.2, Theorems B and C are addressed in Section 5.…”
Section: Statement Of the Main Resultsmentioning
confidence: 99%
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