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    STUDIA MATHEMATICA - Issue no. 4 / 2013  
         
  Article:   NEW ASPECTS IN THE USE OF CANONOID TRANSFORMATIONS.

Authors:  .
 
       
         
  Abstract:   Canonoid transformations with respect to a locally Hamiltonian vector field are studied through the concept of generating function and the Helmholtz theory of the inverse problem. The case of dimension two is connected with the Liouville equation. The use of such transformations for determining first integrals is illustrated with two examples: the Whittaker system (in dimension four) and the damped harmonic oscillator (in the dimension two).

Mathematics Subject Classification (2010): 37C80, 37C05, 37C10, 70H15.
Keywords: Locally Hamiltonian vector field, canonoid transformation, the inverse problem, Helmholtz conditions, integrating factor, generating function, Liouville equation.
 
         
     
         
         
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