Cohomology of Aubry-Mather type
Cohomology of Aubry-Mather type
This chapter defines cohomology of Aubry-Mather type and explains why it implies one of the diffusion mechanisms, after a generic perturbation. The definition of Aubry-Mather type includes a much simpler case, that is when the Aubry set is a hyperbolic periodic orbit, still contained in a normally hyperbolic invariant cylinder. This definition says that each of the two local components of the Aubry set is of Aubry-Mather type. There is another type of bifurcation in which one component of the Aubry set is of Aubry-Mather type with an invariant cylinder and another is a hyperbolic periodic orbit. This can be called the asymmetric bifurcation. This case appears at double resonance, when the shortest loop is simple non-critical.
Keywords: cohomology, Aubry-Mather type, diffusion mechanisms, Aubry set, normally hyperbolic invariant cylinder, hyperbolic periodic orbit, asymmetric bifurcation
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