Abstract
Linearizability for hyperbolic fixed points is shown to be equivalent to the existence of certain invariant foliations. The analogue for partial linearizability of nonhyperbolic fixed points is considered.
We’re sorry, something doesn't seem to be working properly.
Please try refreshing the page. If that doesn't work, please contact support so we can address the problem.
REFERENCES
Belitskii, G. R. (1973). Functional equations and conjugacy of local diffeomorphisms of a finite smoothness class. Funct. Anal. Appl. 7, 268-277.
Belitskii, G. R. (1978). Equivalence and normal forms of germs of smooth mappings. Russ. Math. Surv. 11, 107-177.
Hirsch, M., and Pugh, C. (1970). Stable manifolds and hyperbolic sets. Proc. Symp. Pure Math. 14, 133-163.
Hirsch, M., Pugh, C., and Shub, M. (1977). Invariant Manifolds, Lect. Notes Math., Vol. 583, Springer-Verlag, New York.
Kirchgraber, U., and Palmer, K. J. (1990). Geometry in the neighborhood of invariant manifolds of maps and flows and linearization. Pitman Res. Notes Math. 233.
McSwiggen, P. (1996). A geometric characterization of smooth linearizability. Mich. Math. J. 43, 321-335.
McSwiggen, P. (1998). A geometric characterization of partial linearizability. Mich. Math. J. 45, 3-29.
Pugh, C. unpublished lecture notes.
Pugh, C., and Shub, M. (1970). Linearization of normally hyperbolic diffeomorphisms and flows. Inventiones Math. 10, 187-198.
Shub, M. (1987). Global Stability of Dynamical Systems, Springer-Verlag, New York.
Sell, G. (1985). Smooth linearization near a fixed point. Am. J. Math. 107, 1035-1091.
Sternberg, S. (1957). Local contractions and a theorem of Poincaré. Am. J. Math. 79, 809-824.
Sternberg, S. (1958). On the structure of local homeomorphisms of Euclidean n-space. Am. J. Math. 80, 623-631.
Takens, F. (1971). Partially hyperbolic fixed points. Topology 10, 133-147.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
McSwiggen, P.D. Geometric Implications of Linearizability. Journal of Dynamics and Differential Equations 13, 133–146 (2001). https://doi.org/10.1023/A:1009096532406
Issue Date:
DOI: https://doi.org/10.1023/A:1009096532406