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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
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
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 Green’s functions of the Helmholtz and
, 2008
"... A classical problem of freespace Green’s function G0Λ representations of the Helmholtz equation is studied in various quasiperiodic cases, i.e., when an underlying periodicity is imposed in less dimensions than is the dimension of an embedding space. Exponentially convergent series for the freesp ..."
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A classical problem of freespace Green’s function G0Λ representations of the Helmholtz equation is studied in various quasiperiodic cases, i.e., when an underlying periodicity is imposed in less dimensions than is the dimension of an embedding space. Exponentially convergent series for the free
Integrable Structure of Conformal Field Theory II. Qoperator and DDV equation
, 1996
"... This paper is a direct continuation of [1] where we begun the study of the integrable structures in Conformal Field Theory. We show here how to construct the operators Q \Sigma () which act in highest weight Virasoro module and commute for different values of the parameter . These operators appear ..."
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Cited by 168 (18 self)
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equations of Destride Vega (DDV) [3] for the eigenvalues of the Qoperators. We then use the DDV equation to obtain the asymptotic expansions of the Q  operators at large ; it is remarkable that unlike the expansions of the T operators of [1], the asymptotic series for Q() contains the "
Lindstedt Series for Lower Dimensional Tori
"... Introduction One of the first methods to compute quasiperiodic orbits (i. e. invariant tori with linear motions on them) was the Lindstedt method (see [12] Vol. 2) which produces an expansion of the quasiperiodic orbit with a fixed frequency in powers of a small parameter measuring the distance t ..."
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Cited by 16 (5 self)
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Introduction One of the first methods to compute quasiperiodic orbits (i. e. invariant tori with linear motions on them) was the Lindstedt method (see [12] Vol. 2) which produces an expansion of the quasiperiodic orbit with a fixed frequency in powers of a small parameter measuring the distance
Generalizations of Chromatic Derivatives and Series Expansions
 IEEE TRANSACTIONS ON SIGNAL PROCESSING, VOLUME 58 , ISSUE 3
, 2010
"... Chromatic derivatives and series expansions of bandlimited functions have recently been introduced as an alternative representation to Taylor series and they have been shown to be more useful in practical signal processing applications than Taylor series. Although chromatic series were originally i ..."
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Chromatic derivatives and series expansions of bandlimited functions have recently been introduced as an alternative representation to Taylor series and they have been shown to be more useful in practical signal processing applications than Taylor series. Although chromatic series were originally
1: Fractional Lindstedt series Fractional Lindstedt series
, 2005
"... Abstract. The parametric equations of the surfaces on which highly resonant quasiperiodic motions develop (lowerdimensional tori) cannot be analytically continued, in general, in the perturbation parameter ε, i.e. they are not analytic functions of ε. However rather generally quasiperiodic motions ..."
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Abstract. The parametric equations of the surfaces on which highly resonant quasiperiodic motions develop (lowerdimensional tori) cannot be analytically continued, in general, in the perturbation parameter ε, i.e. they are not analytic functions of ε. However rather generally quasiperiodic
On the Fourier expansions of Eisenstein series of some types
 Georgian Math. J
"... Abstract. Bases of the spaces of Eisenstein series Ek(Γ0(4N), χ) (k ∈ N, k ≥ 3, N is an odd natural and squarefree) and Ek/2(Γ̃0(4N), χ) (k ∈ N, 2 k, k ≥ 5, N is an odd natural and squarefree) are constructed for any Dirichlet character mod 4N and Fourier expansions of these series are obtained. ..."
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Cited by 2 (2 self)
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Abstract. Bases of the spaces of Eisenstein series Ek(Γ0(4N), χ) (k ∈ N, k ≥ 3, N is an odd natural and squarefree) and Ek/2(Γ̃0(4N), χ) (k ∈ N, 2 k, k ≥ 5, N is an odd natural and squarefree) are constructed for any Dirichlet character mod 4N and Fourier expansions of these series are obtained.
Landau Pole and the Nature of 1/Nf Expansion Series in Quantum Electrodynamics
, 2006
"... Dyson has put forward strong arguments to suggest that the perturbation series in quantum electrodynamics can not be convergent. Landau, on the other hand, argued that the effective coupling constant in QED develops a pole at some very high energy scale. We show that these two problems are not entir ..."
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are not entirely independent of each other. Our analysis is centered around 1/Nf expansion series in QED, where Nf, the number of flavours of fermions is very large. PACS numbers: 11.15.Pg, 11.15.Bt, 12.20.Ds, 11.10.Gh Quantum Eletrodynamics (QED) is considered as the most successful of all physical theories
Results 1  10
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669