Invariant normalization of non-autonomous Hamiltonian systems

✍ Scribed by A.G. Petrov

• Book ID: 104142367
• Publisher: Elsevier Science
• Year: 2004
• Tongue: English
• Weight: 714 KB
• Volume: 68
• Category: Article
• ISSN: 0021-8928
• DOI: 10.1016/s0021-8928(04)00049-8

✦ Synopsis

A new method of constructing canonical replacements of variables in parametric form, which differs from the existing constructive methods in the Hamiltonian procedure: the method of derivative functions and the method of generators, is proposed. A criterion of the existence of a parametric representation of the canonical replacement of variables is formulated and the law of the conversion of the Hamiltonian is derived. The method is used to obtain the normal form of Hamiltonians. A definition of the normal form [1, 2] is used which does not require separation into autonomous -non-autonomous and resonance -non-resonance cases and is carried out within a single approach. A system of equations, similar to the chain of equations obtained previously in [1, 2], is derived for the asymptotics of the normal form. Instead of the generator and generating Hamiltonian method a parameterized generating function is used [3], which enables, as in [1, 2], a chain of equations to be obtained directly for the non-autonomous Hamiltonians but without reducing the system to an autonomous form.