Integrable systems in the plane with center type linear part

Javier Chavarriga

Displaying similar documents to “Integrable systems in the plane with center type linear part”

On Baica's trigonometric identity.

Gregorac, R.J. (1989)

International Journal of Mathematics and Mathematical Sciences

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Trigonometric identities.

Baica, Malvina (1986)

International Journal of Mathematics and Mathematical Sciences

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Integrability of a linear center perturbed by a fourth degree homogeneous polynomial.

Javier Chavarriga, Jaume Giné (1996)

Publicacions Matemàtiques

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In this work we study the integrability of a two-dimensional autonomous system in the plane with linear part of center type and non-linear part given by homogeneous polynomials of fourth degree. We give sufficient conditions for integrability in polar coordinates. Finally we establish a conjecture about the independence of the two classes of parameters which appear in the system; if this conjecture is true the integrable cases found will be the only possible ones.

Cubic forms on Riemannian surfaces

Alois Švec (1978)

Časopis pro pěstování matematiky

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Integrability of a linear center perturbed by a fifth degree homogeneous polynomial.

Javier Chavarriga, Jaume Giné (1997)

Publicacions Matemàtiques

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In this work we study the integrability of two-dimensional autonomous system in the plane with linear part of center type and non-linear part given by homogeneous polynomials of fifth degree. We give a simple characterisation for the integrable cases in polar coordinates. Finally we formulate a conjecture about the independence of the two classes of parameters which appear on the system; if this conjecture is true the integrable cases found will be the only possible ones.

Two-dimensional real symmetric spaces with maximal projection constant

Bruce Chalmers, Grzegorz Lewicki (2000)

Annales Polonici Mathematici

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Let V be a two-dimensional real symmetric space with unit ball having 8n extreme points. Let λ(V) denote the absolute projection constant of V. We show that $λ (V) \leq λ (V_{n})$ where $V_{n}$ is the space whose ball is a regular 8n-polygon. Also we reprove a result of [1] and [5] which states that $4 / π = λ (l ₂^{(2)}) \geq λ (V)$ for any two-dimensional real symmetric space V.

On isotropic tensors

H. Fath el Bab (1977)

Czechoslovak Mathematical Journal

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