Uniform hyperbolicity of invariant cylinder (Q2358667)

This paper concerns small perturbations of integrable Hamiltonian systems \(H(p, q)=h(p)+\varepsilon P(p, q)\), \((p, q)\in \mathbb{R}^3\times \mathbb{T}^3\) with 3 degrees of freedom where \(\partial ^2h(p)\) is positive definite and both \(h\) and \(P\) are \(C^r\)-functions with \(r\geq 6\). The main result gives the existence of finitely many normally hyperbolic invariant cylinders for some maps associated with \(H\), where a manifold with boundary is called \textit{cylinder} if it is homeomorphic to the standard cylinder \(\mathbb{T}\times [0, 1]\).