σ-Hölder continuous linearization near hyperbolic fixed points in Rn

Journal of Differential Equations

Volumn 162, Issue 2, 2000, Pages 251-269

  Tan, Bin ^a  

^a GEORGIA INSTITUTE OF TECHNOLOGY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0034629686     PISSN: 00220396     EISSN: None     Source Type: Journal    
DOI: 10.1006/jdeq.1999.3693     Document Type: Article

References (20)

1. S. Kh. Aranson, G. R. Belitsky, and E. V. Zhuzhoma, "Introduction to the qualitative theory of dynamical systems on surfaces," Amer. Math. Soc., 1996.
2. V. I. Arnold, "Geometrical Methods in the Theory of Ordinary Differential Equations," Springer-Verlag, New York, 1983.
3. G. R. Belitskii, Equivalence and normal forms of germs of smooth mappings, Russian Math. Surveys 33 (1978), 107-177.
4. 1 semigroups in Banach spaces, J. Differential Equations 139 (1997), 283-318.
5. S.-N. Chow, X.-B. Lin, and K. Lu, Smooth invariant foliations in infinite dimensional spaces, J. Differential Equations 94 (1991), 266-291.
6. D. M. Grobman, Topological classification of the neighborhood of a singular point in n-dimensional space, Mat. Sb. 56 (1962), 77-94.
7. P. Hartman, On local homeomorphisms of Euclidean spaces, Bol. Soc. Mat. Mexican (3) 5 (1960), 220-241.
8. P. Hartman, On the local linearization of differential equations, Proc. Amer. Math. Soc. 16 (1963), 568-573.
9. P. Hartman, "Ordinary Differential Equations," Wiley, New York, 1964.
10. M. W. Hirsch, C. Pugh, and M. Shub, "Invariant Manifolds," Lecture Notes in Mathematics, Vol. 583, Springer-Verlag, New York, 1977.
11. K. Lu, A Hartman-Grobman theorem for a class of one dimensional parabolic equations, J. Differential Equations.
12. U. Kirchgraber and K. Palmer, "Geometry in the Neighborhood of Invariant Manifolds of Maps and Flows and Linearization," Wiley, New York, 1990.
13. V. Rayskin, α-Hölder linearization, J. Differential Equations, accepted.
14. K. Sakamoto, Smooth linearization of vector fields near invariant manifolds, Hiroshima Math. J. 24, No. 2 (1994), 331-355.
15. G. R. Sell, Smooth linearization near a fixed point, Amer. J. Math. 107 (1985), 1035-1091.
16. n contractions of the real line, Duke Math. J. 24 (1957), 97-102.
17. S. Sternberg, On the structure of local homeomorphism of Euclidean n-space, Amer. J. Math. 80 (1958), 623-631.
18. D. Stowe, Linearization in two dimensions, J. Differential Equations 63 (1989), 183-226.
19. n without nonresonant conditions, draft.
20. S. van Strien, Smooth linearization of hyperbolic fixed points without resonance conditions, J. Differential Equations 85 (1990), 66-90.