11 research outputs found

    Stabilization of heterodimensional cycles

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    Abstract. We consider diffeomorphisms f with heteroclinic cycles associated to saddles P and Q of different indices. We say that a cycle of this type can be stabilized if there are diffeomorphisms close to f with a robust cycle associated to hyperbolic sets containing the continuations of P and Q. We focus on the case where the indices of these two saddles differ by one. We prove that, excluding one particular case (so-called twisted cycles that additionally satisfy some geometrical restrictions), all such cycles can be stabilized

    Stabilization of heterodimensional cycles

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    We consider diffeomorphisms ff with heteroclinic cycles associated to saddles PP and QQ of different indices. We say that a cycle of this type can be stabilized if there are diffeomorphisms close to ff with a robust cycle associated to hyperbolic sets containing the continuations of PP and QQ. We focus on the case where the indices of these two saddles differ by one. We prove that, excluding one particular case (so-called twisted cycles that additionally satisfy some geometrical restrictions), all such cycles can be stabilized.Comment: 31 pages, 9 figure
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