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Nonexistence of formal first integrals for nonlinear systems under resonance
Non-integrability Resonance First integral Normal form
2011/10/12
In this paper, by using normal form theory we give some criteria of nonexistence of formal first integrals for general nonlinear systems under resonance. As application, we also give a criterion for n...
We consider systems of ordinary differential equations with known first integrals. The notion of a discrete tangent space is introduced as the orthogonal complement of an arbitrary set of discrete gr...
Computation of Darboux polynomials and rational first integrals with bounded degree in polynomial time
Darboux polynomials rational first integrals bounded degree
2010/12/7
In this paper we study planar polynomial differential systems of this form: dX dt = ˙X = A(X, Y ),dY dt = ˙Y = B(X, Y ),where A,B ∈ Z[X, Y ] and deg A ≤ d, degB ≤ d, kAk1 ≤ H and kBk1 ≤H. A lot of pro...
Discrete Variation Principle and First Integrals of Lagrange-Maxwell Mechanico-Electrical Dynamical Systems
discrete variational principle first integral mechanico-electrical system
2012/8/1
We give discrete variational principle and integral algorithm for the finite dimensional Lagrange-Maxwell mechanico-electrical system, which includes nonconservative force and dissipative function. Th...