Affiliation:
1. Department of Mathematics, Southeast University, Nanjing 210096, China
Abstract
Abstract
In this paper we are mainly concerned with the persistence of invariant tori with prescribed frequency
for analytic nearly integrable Hamiltonian systems under the Brjuno–Rüssmann non-resonant condition,
when the Kolmogorov non-degeneracy condition is violated.
As it is well known, the frequency of the persisting invariant tori may undergo some drifts, when the Kolmogorov non-degeneracy condition is violated.
By the method of introducing external parameters and rational approximations,
we prove that if the Brouwer topological degree of the frequency mapping is nonzero at some Brjuno–Rüssmann
frequency, then the invariant torus with this frequency persists under small perturbation.
Funder
National Natural Science Foundation of China
Natural Science Foundation of Jiangsu Province
Subject
General Mathematics,Statistical and Nonlinear Physics
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