Extension of invariant manifolds and applications. (English) Zbl 1083.37026
Summary: We state an extension theorem for invariant manifolds of diffeomorphisms near a normally hyperbolic invariant torus. We apply this result in particular to the resolution of equations \({\mathcal L}_{U_j}(f)= \theta_j\), \(1\leq j\leq n-1,\) where the \(U_j\)’s are linear diagonal vector fields and the \(\theta_j\)’s are germs at 0 of smooth functions on \(\mathbb{R}^n\).
MSC:
| 37D10 | Invariant manifold theory for dynamical systems |
References:
| [1] | B. Abbaci, Variétés invariantes et applications, Thèse, Université Paris 7, 2001; B. Abbaci, Variétés invariantes et applications, Thèse, Université Paris 7, 2001 |
| [2] | B. Abbaci, An extension theorem for invariant manifold and some applications, in preparation; B. Abbaci, An extension theorem for invariant manifold and some applications, in preparation · Zbl 1083.37026 |
| [3] | Chaperon, M., Géométrie différentielle et singularités de systèmes dynamiques, Astérisque, 138-139 (1986) · Zbl 0601.58002 |
| [4] | Dufour, J. P., Hyperbolic actions of \(R^p\) on Poisson manifolds, (Dazord, P.; Weinstein, A., Symplectic Geometry, Groupoids and Integrable Systems. Symplectic Geometry, Groupoids and Integrable Systems, Math. Sci. Res. Inst. Publ., vol. 20 (1989), Springer: Springer New York), 137-150 · Zbl 0732.57016 |
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