Erratum to: 2-D Duffing Oscillator: Elliptic Functions from a Dynamical Systems Point of View

Molero, Francisco Javier; Lara, Martı́n; Ferrer, S.; Céspedes, Francisco

doi:10.1007/s12346-013-0098-0

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“…Moreover, as an alternative to confront directly with hyperelliptic functions, we propose to experiment with reparametrizations starting from low dimensions. More precisely, we extend the regularization dv * = ω 3 dv, already studied for the case N = 3 by Molero et al [12]. This way of proceeding seems to be an open line of work.…”

Section: Integrals Functions and Regularizationmentioning

confidence: 92%

“…In what follows we are going to proceed making use of the regularization. To do that, we start remembering in Section 5.1 the recent proposal of the authors for N = 3 (see Molero et al [12]), which is intrinsically connected with the Jacobi amplitude. After that we develop the same approach for the N = 4 case.…”

Section: Regularization and 'Generalized Amplitudes' For The Mahler S...mentioning

confidence: 99%

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On the $$\varvec{N}$$ N -extended Euler system: generalized Jacobi elliptic functions

2016

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We study the integrable system of first order differential equations ω i (v) = α i j =i ω j (v), (1 ≤ i, j ≤ N ) as an initial value problem, with real coefficients α i and initial conditions ω i (0). The analysis is based on its quadratic first integrals. For each dimension N , the system defines a family of functions, generically hyperelliptic functions. When N = 3, this system generalizes the classic Euler system for the reduced flow of the free rigid body problem, thus we call it N -extended Euler system (N -EES). In this Part I the cases N = 4 and N = 5 are studied, generalizing Jacobi elliptic functions which are defined as a 3-EES. Taking into account the nested structure of the N -EES, we propose reparametrizations of the type dv * = g(ω i ) dv that separate geometry from dynamic. Some of those parametrizations turn out to be generalization of the Jacobi amplitude. In Part II we consider geometric properties of the N -system and the numeric computation of the functions involved. It will be published elsewhere.keywords: Integrable systems Generalized Euler system Jacobi and Weierstrass elliptic functions third Legendre elliptic integral arXiv:1505.06142v1 [math.DS]

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Section: Integrals Functions and Regularizationmentioning

confidence: 92%

Section: Regularization and 'Generalized Amplitudes' For The Mahler S...mentioning

confidence: 99%

On the $$\varvec{N}$$ N -extended Euler system: generalized Jacobi elliptic functions

2016

Self Cite

View full text Add to dashboard Cite

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Erratum to: 2-D Duffing Oscillator: Elliptic Functions from a Dynamical Systems Point of View

Cited by 1 publication

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On the $$\varvec{N}$$ N -extended Euler system: generalized Jacobi elliptic functions

On the $$\varvec{N}$$ N -extended Euler system: generalized Jacobi elliptic functions

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