Displaying similar documents to “Integrability of a linear center perturbed by a fifth degree homogeneous polynomial.”

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.

Integrable systems in the plane with center type linear part

Javier Chavarriga (1994)

Applicationes Mathematicae

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We study integrability of two-dimensional autonomous systems in the plane with center type linear part. For quadratic and homogeneous cubic systems we give a simple characterization for integrable cases, and we find explicitly all first integrals for these cases. Finally, two large integrable system classes are determined in the most general nonhomogeneous cases.

Carleman estimates for a subelliptic operator and unique continuation

Nicola Garofalo, Zhongwei Shen (1994)

Annales de l'institut Fourier

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We establish a Carleman type inequality for the subelliptic operator ℒ = Δ z + | x | 2 ∂ t 2 in ℝ n + 1 , n ≥ 2 , where z ∈ ℝ n , t ∈ ℝ . As a consequence, we show that - ℒ + V has the strong unique continuation property at points of the degeneracy manifold { ( 0 , t ) ∈ ℝ n + 1 | t ∈ ℝ } if the potential V is locally in certain L p spaces.