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Title:
Symplectic geometry of hyperbolic cylinders and their homoclinic intersections
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Abstract:
Abstract: We first examine the existence, uniqueness, regularity, twist and symplectic properties of compact invariant cylinders with boundary, located near simple or double resonances in perturbations of action-angle systems on the annulus $A^3$. We then prove they satisfy sufficient compatibility conditions on their dynamics and their homoclinic intersections, in order to prove the existence of drifting orbits along them, shadowing pseudo-orbits of inner-homoclinic polysystems. This provides us with a good control of the local behavior of the drifting orbits near essential hyperbolic 2-dimensional tori located inside the cylinders.
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