A New Topological Invariant of Hamiltonian Systems of Liouville-Integrable Differential Equations. An Invariant Portrait of Integrable Equations and Hamiltonians

1988 ◽  
pp. 300-325 ◽  
Author(s):  
A. T. Fomenko
Keyword(s):  
Differential Equations ◽  
Hamiltonian Systems ◽  
Topological Invariant ◽  
Integrable Equations ◽  
Liouville Integrable

INTEGRABILITY AND ACTION FUNCTION IN MULTI-HAMILTONIAN SYSTEMS

2004 ◽  
Vol 19 (11) ◽  
pp. 863-870 ◽  
Author(s):  
S. I. MUSLIH
Keyword(s):  
Differential Equations ◽  
Hamiltonian Systems ◽  
Equations Of Motion ◽  
Integral Function ◽  
Jacobi Method ◽  
Action Function ◽  
Action Integral ◽  
Method Integration ◽  
Total Differential

Multi-Hamiltonian systems are investigated by using the Hamilton–Jacobi method. Integration of a set of total differential equations which includes the equations of motion and the action integral function is discussed. It is shown that this set is integrable if and only if the total variations of the Hamiltonians vanish. Two examples are studied.

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