A completely integrable case in three-particle problems with homogeneous potentials

1986 ◽  
Vol 12 (4) ◽  
pp. 267-275 ◽  
Author(s):  
P. P. Fiziev
Keyword(s):  
Integrable Case ◽  
Completely Integrable ◽  
Homogeneous Potentials

On the completely integrable case of the Rössler system

2012 ◽  
Vol 53 (5) ◽  
pp. 052701 ◽  
Author(s):  
Răzvan M. Tudoran ◽  
Anania Gîrban
Keyword(s):  
Integrable Case ◽  
Completely Integrable ◽  
Rossler System ◽  
Rössler System

An L–A pair for the Hess–Apel'rot system and a new integrable case for the Euler–Poisson equations on so(4) × so(4)

2001 ◽  
Vol 131 (4) ◽  
pp. 845-855 ◽  
Author(s):  
Vladimir Dragović ◽  
Borislav Gajić
Keyword(s):  
Three Dimensional ◽  
Classification Theorem ◽  
Geometric Integration ◽  
Integrable Case ◽  
Integration Procedure ◽  
Completely Integrable ◽  
Poisson Equations ◽  
Corrected Version ◽  
Explicit Formulae

We present an L–A pair for the Hess–Apel'rot case of a heavy rigid three-dimensional body. Using it, we give an algebro-geometric integration procedure. Generalizing this L–A pair, we obtain a new completely integrable case of the Euler–Poisson equations in dimension four. Explicit formulae for integrals that are in involution are given. This system is a counterexample to one of Ratiu's theorems. A corrected version of this classification theorem is proved.

scholarly journals L p Norms of Eigenfunctions in the Completely Integrable Case

2003 ◽  
Vol 4 (2) ◽  
pp. 343-368 ◽  
Author(s):  
J. A. Toth ◽  
S. Zelditch
Keyword(s):  
Integrable Case ◽  
Completely Integrable

A completely integrable case in the complex Lorenz equations

1991 ◽  
Vol 154 (3-4) ◽  
pp. 127-130 ◽  
Author(s):  
G.P. Flessas ◽  
P.G.L. Leach
Keyword(s):  
Integrable Case ◽  
Lorenz Equations ◽  
Completely Integrable

scholarly journals A completely integrable case in the complex Lorenz equations

2020 ◽  
Vol 1 ◽  
pp. 126
Author(s):  
G. P. Flessas ◽  
P. G.L. Leach
Keyword(s):  
Exact Solution ◽  
Elliptic Functions ◽  
Integrable Case ◽  
Lie Theory ◽  
Lorenz Equations ◽  
Jacobian Elliptic Functions ◽  
Completely Integrable ◽  
Parameter Values

By application of the Lie theory of extended groups and for the parameter values σ=1/2, b=1, r1= e^2/2, r2=e/2, e arbitrary we prove that the system of the complex Lorenz equations is algebraically completely integrable. The respective general exact solution i$ expressed by means of Jacobian elliptic functions

scholarly journals Transverse Hilbert schemes and completely integrable systems

2017 ◽  
Vol 4 (1) ◽  
pp. 263-272 ◽  
Author(s):  
Niccolò Lora Lamia Donin
Keyword(s):  
Integrable Systems ◽  
Hilbert Scheme ◽  
Symplectic Form ◽  
Initial Surface ◽  
Hilbert Schemes ◽  
Completely Integrable Systems ◽  
Completely Integrable ◽  
Symplectic Surface ◽  
Complex Symplectic ◽  
Minimum Polynomial

Abstract In this paper we consider a special class of completely integrable systems that arise as transverse Hilbert schemes of d points of a complex symplectic surface S projecting onto ℂ via a surjective map p which is a submersion outside a discrete subset of S. We explicitly endow the transverse Hilbert scheme Sp[d] with a symplectic form and an endomorphism A of its tangent space with 2-dimensional eigenspaces and such that its characteristic polynomial is the square of its minimum polynomial and show it has the maximal number of commuting Hamiltonians.We then provide the inverse construction, starting from a 2ddimensional holomorphic integrable system W which has an endomorphism A: TW → TW satisfying the above properties and recover our initial surface S with W ≌ Sp[d].

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