INFINITY MANIFOLDS OF CUBIC POLYNOMIAL HAMILTONIAN VECTOR FIELDS WITH 2 DEGREES OF FREEDOM

2000 ◽  
Author(s):  
MANUEL FALCONI ◽  
ERNESTO A. LACOMBA ◽  
JAUME LLIBRE
Keyword(s):  
Degrees Of Freedom ◽  
Vector Fields ◽  
Hamiltonian Vector ◽  
Hamiltonian Vector Fields ◽  
Cubic Polynomial

scholarly journals Hamiltonian Vector Fields on Weil Bundles

2015 ◽  
Vol 7 (3) ◽  
Author(s):  
Norbert Mahoungou Moukala ◽  
Basile Guy Richard Bossoto
Keyword(s):  
Vector Fields ◽  
Hamiltonian Vector ◽  
Hamiltonian Vector Fields

A weight-homogenous condition to the real Jacobian conjecture in

2021 ◽  
pp. 1-9
Author(s):  
Francisco Braun ◽  
Claudia Valls
Keyword(s):  
Differential Equations ◽  
Vector Fields ◽  
Qualitative Theory ◽  
Hamiltonian Vector ◽  
Jacobian Conjecture ◽  
Local Diffeomorphism ◽  
The Real ◽  
Hamiltonian Vector Fields ◽  
Real Linear

Abstract It is known that a polynomial local diffeomorphism $(f,\, g): {\mathbb {R}}^{2} \to {\mathbb {R}}^{2}$ is a global diffeomorphism provided the higher homogeneous terms of $f f_x+g g_x$ and $f f_y+g g_y$ do not have real linear factors in common. Here, we give a weight-homogeneous framework of this result. Our approach uses qualitative theory of differential equations. In our reasoning, we obtain a result on polynomial Hamiltonian vector fields in the plane, generalization of a known fact.

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