Do Average Hamiltonians Exist?

Details Do Average Hamiltonians Exist? Do Average Hamiltonians Exist?

Jan 1999

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1999cemda..73..243f&link_type=abstract

Celestial Mechanics and Dynamical Astronomy, v. 73, Issue 1/4, p. 243-248 (1999).

Astronomy and Astrophysics

Astronomy

1

Scientific paper

The word "average" and its variations became popular in the sixties and implicitly carried the idea that "averaging" methods lead to "average" Hamiltonians. However, given the Hamiltonian H = H0(J) + ∈R(θ, J), (∈ < < 1), the problem of transforming it into a new Hamiltonian H* (J*) (dependent only on the new actions J*), through a canonical transformation given by zero-average trigonometrical series has no general solution at orders higher than the first.

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