Persistence of the hyperbolic lower dimensional non-twistinvariant torus in a class of Hamiltonian systems

Lei  Wang; Quan  Yuan; Jia  Li

doi:10.3934/cpaa.2016.15.1233

Article Contents

2016, Volume 15, Issue 4: 1233-1250. Doi: 10.3934/cpaa.2016.15.1233

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Persistence of the hyperbolic lower dimensional non-twist invariant torus in a class of Hamiltonian systems

1.
Department of Mathematics and Physics, Hefei University, Hefei, MO 230601
2.
School of Machinery and Electronic Information, China University of Geosciences, Wuhan, MO 430074
3.
School of Mathematical Physics, Xuzhou Institute of Technology, Xuzhou, MO 221000

Received: July 31, 2015

Revised: January 31, 2016

Published: June 2016

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Abstract

We consider a class of nearly integrable Hamiltonian systems with Hamiltonian being $H(\theta,I,u,v)=h(I)+\frac{1}{2}\sum_{j=1}^{m}\Omega_j(u_j^2-v_j^2)+f(\theta,I,u,v)$. By introducing external parameter and KAM methods, we prove that, if the frequency mapping has nonzero Brouwer topological degree at some Diophantine frequency, the hyperbolic invariant torus with this frequency persists under small perturbations.

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Mathematics Subject Classification: Primary: 37-XX, 70-XX; Secondary: 70H08.

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