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作者:Marcel Guardia , Vadim Kaloshin , Jianlu Zhang
来源:[J].Archive for Rational Mechanics and Analysis(IF 2.292), 2019, Vol.233 (2), pp.799-836Springer
摘要:Abstract(#br)For the Restricted Circular Planar 3 Body Problem, we show that there exists an open set $${\mathcal{U}}$$ U in phase space of fixed measure, where the set of initial points which lead to collision is $${O(\mu^\frac{1}{20})}$$ O ( μ 1 20 ) dense as $${\mu\righta...
作者:Marcel Guardia
来源:[J].Communications in Mathematical Physics(IF 1.971), 2014, Vol.329 (1), pp.405-434Springer
摘要:Abstract(#br)Fix s > 1. Colliander et al. proved in (Invent Math 181:39–113, 2010 ) the existence of solutions of the cubic defocusing nonlinear Schrödinger equation in the two torus whose s -Sobolev norm undergoes arbitrarily large growth as time evolves. In this paper we g...
作者:... Ernest Fontich , Marcel Guardia , Tere M. Seara
来源:[J].Journal of Differential Equations(IF 1.48), 2012, Vol.253 (12), pp.3304-3439Elsevier
摘要:Abstract(#br)We study the problem of exponentially small splitting of separatrices of one degree of freedom classical Hamiltonian systems with a non-autonomous perturbation fast and periodic in time. We provide a result valid for general systems which are algebraic or trigon...
作者:Marcel Guardia , Tere M Seara
来源:[J].Nonlinearity(IF 1.602), 2012, Vol.25 (5), pp.1367-1412IOP
摘要:In this paper, we study the splitting of separatrices phenomenon which arises when one considers a Hamiltonian system of one degree of freedom with a fast periodic or quasiperiodic and meromorphic in the state variables perturbation. The obtained results are different from the pr...

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