6533b82bfe1ef96bd128e2f6
RESEARCH PRODUCT
Stabilization of heterodimensional cycles
Lorenzo J. DíazChristian BonattiShin Kirikisubject
Pure mathematicsMathematics::Dynamical Systems37C29 37D20 37D30Applied MathematicsFOS: MathematicsGeneral Physics and AstronomyStatistical and Nonlinear PhysicsDynamical Systems (math.DS)Mathematics - Dynamical SystemsType (model theory)Focus (optics)Mathematical PhysicsMathematicsdescription
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.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2011-04-05 | Nonlinearity |