Fathi, Albert; Giuliani, Alessandro; Sorrentino, Alfonso Uniqueness of invariant Lagrangian graphs in a homology or a cohomology class. (English) Zbl 1192.37086 Ann. Sc. Norm. Super. Pisa, Cl. Sci. (5) 8, No. 4, 659-680 (2009). In the framework of Hamiltonian systems on the cotangent bundle of a compact manifold it is proved the uniqueness of certain ergodic invariant Lagrangian graphs within a given homology or cohomology class. For quasi-integrable Hamiltonian systems, this implies the global uniqueness of Lagrangian KAM tori with given rotation vector. Reviewer: Mircea Crâşmăreanu (Iaşi) Cited in 9 Documents MSC: 37J50 Action-minimizing orbits and measures (MSC2010) 37J40 Perturbations of finite-dimensional Hamiltonian systems, normal forms, small divisors, KAM theory, Arnol’d diffusion 53D12 Lagrangian submanifolds; Maslov index Keywords:invariant Lagrangian graph; homology or cohomology class PDFBibTeX XMLCite \textit{A. Fathi} et al., Ann. Sc. Norm. Super. Pisa, Cl. Sci. (5) 8, No. 4, 659--680 (2009; Zbl 1192.37086) Full Text: DOI arXiv