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An invitation to singular symplectic geometry
(2017)
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Accés obertIn this paper we analyze in detail a collection of motivating examples to consider bm- symplectic forms and folded-type symplectic structures. In particular, we provide models in Celestial Mechanics for every bm-symplectic ... -
Breakdown of homoclinic orbits to L3 in the RPC3BP (II). An asymptotic formula
(2021-07-21)
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Accés obertThe Restricted 3-Body Problem models the motion of a body of negligible mass under the gravitational influence of two massive bodies called the primaries. If one assumes that the primaries perform circular motions and that ... -
Examples of integrable and non-integrable systems on singular symplectic manifolds
(2016-12)
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Accés obertWe present a collection of examples borrowed from celes- tial mechanics and projective dynamics. In these examples symplectic structures with singularities arise naturally from regularization trans- formations, Appell's ... -
Exponentially small splitting of separatrices and transversality associated to whiskered tori with quadratic frequency ratio
(2015)
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Accés obertThe splitting of invariant manifolds of whiskered (hyperbolic) tori with two frequencies in a nearly-integrable Hamiltonian system, whose hyperbolic part is given by a pendulum, is studied. -
Exponentially small splitting of separatrices associated to 3D whiskered tori with cubic frequencies
(2019-06)
Report de recerca
Accés obertWe study the splitting of invariant manifolds of whiskered (hyperbolic) tori with three frequencies in a nearly-integrable Hamiltonian system, whose hyperbolic part is given by a pendulum. We consider a 3-dimensional ...