Exact smooth classification of hamiltonian vector fields on two-dimensional manifolds

1997 ◽  
Vol 61 (2) ◽  
pp. 146-163 ◽  
Author(s):  
B. S. Kruglikov
Keyword(s):  
Vector Fields ◽  
Hamiltonian Vector ◽  
Two Dimensional ◽  
Hamiltonian Vector Fields ◽  
Smooth Classification

scholarly journals SYMPLECTIC GEOMETRY ON QUANTUM PLANE

1999 ◽  
Vol 14 (08n09) ◽  
pp. 549-557
Author(s):  
SERGIO ALBEVERIO ◽  
SHAO-MING FEI
Keyword(s):  
Symplectic Geometry ◽  
Vector Fields ◽  
Three Dimensional ◽  
Hamiltonian Vector ◽  
Quantum Plane ◽  
Two Dimensional ◽  
Quantum Sphere ◽  
Symplectic Forms ◽  
Hamiltonian Vector Fields

A study of symplectic forms associated with two-dimensional quantum planes and the quantum sphere in a three-dimensional orthogonal quantum plane is provided. The associated Hamiltonian vector fields and Poissonian algebraic relations are made explicit.

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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