American Institute of Mathematical Sciences

July  2016, 15(4): 1233-1250. doi: 10.3934/cpaa.2016.15.1233

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, China 2 School of Machinery and Electronic Information, China University of Geosciences, Wuhan, MO 430074, China 3 School of Mathematical Physics, Xuzhou Institute of Technology, Xuzhou, MO 221000, China

Received  August 2015 Revised  February 2016 Published  April 2016

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.
Citation: Lei Wang, Quan Yuan, Jia Li. Persistence of the hyperbolic lower dimensional non-twist invariant torus in a class of Hamiltonian systems. Communications on Pure & Applied Analysis, 2016, 15 (4) : 1233-1250. doi: 10.3934/cpaa.2016.15.1233
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