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Methods in the Theory of Quasi Periodic Motions
, 1996
"... . Recent results on the theory of the HamiltonJacobi equation and the regularity of their solutions, in spite of the non regularity of the data, are reviewed, and discussed with attention to the cancellation mechanisms that make regularity possible. x1 The Hamilton Jacobi equation. This review de ..."
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. Recent results on the theory of the HamiltonJacobi equation and the regularity of their solutions, in spite of the non regularity of the data, are reviewed, and discussed with attention to the cancellation mechanisms that make regularity possible. x1 The Hamilton Jacobi equation. This review deals on the work developed in collaboration with F.Bonetto, G. Gentile, V. Mastropietro. The Hamilton Jacobi equation for an invariant torus in a ` dimensional hamiltonian system close to an integrable system takes one of the forms: (! 0 \Delta @) 2 h(/) = " (@f)(/ + h(/)) (! 0 \Delta @)h(/) = " f (/ + h(/)) + N (1:1) where / is a point on the `dimensional torus, h(/) a R ` valued function, f; f are functions on T ` , N is a vector in R ` and ! 0 is a diophantine vector in R ` such that, considering the integer components lattice Z ` , there are constants C; ø ? 0 with: Cj! 0 \Delta j jj \Gammaø 8 2 Z ` ; 6= 0 (1:2) where jj = p 2 1 + : : :. The gradient @f is eva...
Absolutely Convergent Series Expansions For Quasi Periodic Motions
, 1996
"... this paper we shall describe the Lindstedt series together with a natural quasiperiodic series expansion, and we shall explain why it is absolutely divergent. We shall then describe a large class of compensations for the terms in the series expansion, and by taking into account these compensations, ..."
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Cited by 81 (0 self)
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this paper we shall describe the Lindstedt series together with a natural quasiperiodic series expansion, and we shall explain why it is absolutely divergent. We shall then describe a large class of compensations for the terms in the series expansion, and by taking into account these compensations
Chaos and QuasiPeriodic Motions on the Homoclinic Surface of Nonlinear Hamiltonian Systems With Two Degrees of Freedom
"... The numerical prediction of chaos and quasiperiodic motion on the homoclinic surface of a ..."
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The numerical prediction of chaos and quasiperiodic motion on the homoclinic surface of a
Periodic and quasiperiodic motions of a solar sail around the family
 S L1 on the Sun  Earth
, 2010
"... Solar sails are a proposed form of spacecraft propulsion using large membrane mirrors to propel a satellite taking advantage of the solar radiation pressure. To model the dynamics of a solar sail we have considered the Earth Sun Restricted Three Body Problem including the Solar radiation pressure ( ..."
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Cited by 5 (3 self)
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. For different fixed sail orientations we find families of planar, vertical and Halotype orbits. We have also computed the centre manifold around different equilibria and used it to describe the quasiperiodic motion around them. We show how the geometry of the phase space varies when we vary the sail
Quasiperiodic motions in dynamical systems. Review of a renormalisation group approach
, 2009
"... Power series expansions naturally arise whenever solutions of ordinary differential equations are studied in the regime of perturbation theory. In the case of quasiperiodic solutions the issue of convergence of the series is plagued of the socalled small divisor problem. In this paper we review a ..."
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Cited by 11 (6 self)
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Power series expansions naturally arise whenever solutions of ordinary differential equations are studied in the regime of perturbation theory. In the case of quasiperiodic solutions the issue of convergence of the series is plagued of the socalled small divisor problem. In this paper we review a
Quasiperiodic motions in strongly dissipative forced systems Guido
"... We consider a class of ordinary differential equations describing onedimensional systems with a quasiperiodic forcing term and in the presence of large damping. We discuss the conditions to be assumed on the mechanical force and the forcing term for the existence of quasiperiodic solutions which ..."
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We consider a class of ordinary differential equations describing onedimensional systems with a quasiperiodic forcing term and in the presence of large damping. We discuss the conditions to be assumed on the mechanical force and the forcing term for the existence of quasiperiodic solutions which
Quasiperiodic motions in strongly dissipative forced systems Guido
"... We consider a class of ordinary differential equations describing onedimensional systems with a quasiperiodic forcing term and in the presence of large damping. We discuss the conditions to be assumed on the mechanical force and the forcing term for the existence of quasiperiodic solutions which ..."
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We consider a class of ordinary differential equations describing onedimensional systems with a quasiperiodic forcing term and in the presence of large damping. We discuss the conditions to be assumed on the mechanical force and the forcing term for the existence of quasiperiodic solutions which
Editor: G. Gallavotti ON CLASSICAL SERIES EXPANSIONS FOR QUASI{PERIODIC MOTIONS
"... Abstract. We reconsider the problem of convergence of classical expansions in a parameter " for quasiperiodic motions on invariant tori in nearly integrable Hamiltonian systems. Using a reformulation of the algorithm proposed by Kolmogorov, we show that if the frequencies satisfy the nonresonan ..."
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Abstract. We reconsider the problem of convergence of classical expansions in a parameter " for quasiperiodic motions on invariant tori in nearly integrable Hamiltonian systems. Using a reformulation of the algorithm proposed by Kolmogorov, we show that if the frequencies satisfy
Quasiperiodic Motions of a Rigid Body II  Implications for the Original System
, 1999
"... This is a sequel to [Hanmann;97]. The original system, while being an "perturba tion of the Euler top, is " 2 close to its normal form approximation. The normal form automatically `removes the degeneracy' of the superintegrable Euler top and KAMtheory allows to conclude that a l ..."
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]. The rigid body motion along such 2tori closely follows the rotationalprecessional motion of the Euler top. 1. The normal form Let us describe the averaged flow on a fixed energy shell. Indeed, the energy shells f H(jj; ; =; ae; 1 ; 2 ; 3 ) = h g fill up the phase space in a trivial way. Recall from
Article DriftFree Position Estimation of Periodic or QuasiPeriodic Motion Using Inertial Sensors
, 2011
"... sensors ..."
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