Cohomology equations near hyperbolic points and geometric versions of sternberg linearization theorem

Journal of Geometric Analysis

Volumn 6, Issue 4, 1996, Pages 613-649

  Banyaga, A ^b   De La Llave, R ^b   Wayne, C E ^a  

^a Boston University   (United States)

^b NONE

Author keywords

Contact gormetry; Linearization; Normal form; Symplectic; Volume preserving deformation

Indexed keywords

EID: 8744288727     PISSN: 10506926     EISSN: None     Source Type: Journal    
DOI: 10.1007/bf02921624     Document Type: Article

References (34)

1. [B] Belitskii, A. Equivalence and normal forms of germs of smooth mappings. Russ. Math. Surv: 33, 107-177 (1978).
2. [BLW] Banyaga, A., de la Llave, R., and Wayne, C. E. Cohomology equations and commutators of germs of contact diffeomorphisms. Trans. A.M.S. 312, 755-778 (1989).
3. [Bi] ElBialy, M. S. Linearization of vector fields near resonant hyperbolic rest points. Preprint.
4. [Ch] Chaperon, M. Géométrie differéntielle et singularités des systèmes dynamiques. Astérisque 138-139 (1986).
5. [Che] Chen, K. T. Equivalence and decomposition of vector fields about an elementary critical point. Amer. J. Math. 85, 693-722 (1963).
6. [CM] Chernoff, P., and Marsden, J. Properties of infinite dimensional hamiltonian systems. Lecture Notes in Math., vol. 425. Springer-Verlag, New York, 1974.
7. [DL] Delshams, A., and de la Llave, R. Some algorithms for computations of normal forms and their object oriented implementation. Manuscript.
8. [Gr] Grey, J. Some global properties of contact structures. Ann. of Math. 69, 421-450 (1959).
9. [Har] Hartman, P. Ordinary Differential Equations. Birkhauser, Boston, 1982.
10. [I] Ilyashenko, Y., and Yakovenko, S. Finitely smooth normal forms of local families of diffeomorphisms and vector fields. Russ. Mat. Surv: 46, 1-43 (1991).
11. [Jo] Journé, J-L. A regularity lemma for functions of several variables. Rev. Mat. Iber. 4, 187-193 (1988).
12. [Kr] Krantz, S. Lipschitz spaces, smoothness of functions and approximation theory. Expo. Mat. 1, 193-260 (1983).
13. [La] Lanford, O. Bifurcation of periodic solutions into invariant tori: The work of Ruelle and Takens. Lecture Notes in Math., vol. 322. Springer-Verlag, New York, 1972.
14. [Le] Levine, H. I. Singularities of differentiate mappings, notes of a course by R. Thom. In Singularities at Liverpool I, edited by C. T. Wall, Lecture Notes in Math., vol. 192. Springer-Verlag, Berlin, 1971.
15. [Li] Liberman, P. Sur les automorphismes infinitesimaux des structures symplectiques et des structure de contact. Colloque de Geometrie différentielle globale Bruxelles 1958. Louvain, 1959.
16. [Li2] Liberman, P., and Marle, Ch-M. Symplectic Geometry and Analytical Mechanics. D. Reidel, Dordrecht, 1987.
17. [LW] de la Llave, R., and Wayne, C. E. On Irwin's proof of the pseudostable manifold theorem. Math. Zeit. 219, 301-321 (1995).
18. [LMM] de la Llave, R., Marco, J. M., and Moriyón, R. Canonical perturbation theories of Anosov diffeomorphisms and regularity results for the Livsic cohomology equation. Ann. of Math. 123, 537-611 (1986).
19. [Ly] Lychiagin, V. V. On sufficient orbits of a group of contact diffeomorphisms. Math. USSR Sbornik 33, 233-242 (1977).
20. [M] Marsden, J. Applications of Global Analysis in Mathematical Physics. Publish or Perish, Waltham, MA, 1974.
21. ∞ mappings II: Infinitesimal stability implies stability. Ann. of Math. 89, 254-291 (1969).
22. [Mi] Milnor, J. Topology from a Differentiable Viewpoint. University of Virginia Press, Charlottesville, VA, 1965.
23. [Mo] Moser, J. Proof of a generalized form of a fixed point theorem. In: Geometry and Topology Rio 1976, edited by J. Palis and M. do Carmo, Lecture Notes in Math., vol. 597. Springer-Verlag, New York, 1977.
24. [Mo2] Moser, J. On the volume elements of a manifold. Trans. Amer. Math. Soc. 120, 286-294 (1965).
25. [Mo3] Moser, J. The analytic invariants of an area preserving mapping near a hyperbolic fixed point. Comm. Pure Appl. Math. 9, 673-693 (1956).
26. [Ni] Nitecki, Z. Differentiable Dynamics. MIT Press, Cambridge, MA, 1971.
27. [Pa] Palis, J. On the local structure of hyperbolic fixed points in Banach spaces. Anais Acad. Brazil 40 (1968).
28. [Ro] Roussarie, R. Modèles locaux des champs et des formes. Asterisque 30 (1975).
29. [Ru] Ruelle, D. Elements of Differential Dynamics and Bifurcation Theory. Academic Press, New York, 1990.
30. [Sp] Spivak, M. Calculus on Manifolds. Benjamin, 1965.
31. [St] Sternberg, S. On the structure of local homeomorphisms II. Amer. J. Math. 80, 623-632 (1958).
32. [St2] Sternberg, S. Infinite Lie groups and the formal aspects of dynamical systems. J. Math. Mech. 10, 451-474 (1961)
33. [St3] Sternberg, S. The structure of local homeomorphism III. Amer. J. Math. 81, 578-604 (1959).
34. [Ta] Takens, F. Singularities of vector fields. Pub. Mat. IHES 43, 47-100 (1974).