On exponentially attracting invariant manifolds of ODEs

Nonlinearity

Volumn 16, Issue 1, 2003, Pages 147-160

  Ryashko, L B ^a   Shnol, E E ^b  

^a URAL FEDERAL UNIVERSITY   (Russian Federation)

^b INSTITUTE OF MATHEMATICAL PROBLEMS OF BIOLOGY   (Russian Federation)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0242339744     PISSN: 09517715     EISSN: None     Source Type: Journal    
DOI: 10.1088/0951-7715/16/1/310     Document Type: Article

References (14)

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3. Hirsch M W, Pugh C C and Shub M 1977 Invariant Manifolds (Berlin: Springer)
4. Wiggins S 1994 Normally Hyperbolic Invariant Manifolds in Dynamical Systems (Berlin: Springer)
5. Kirchgaber U and Palmer K J 1990 Geometry in the Neighborhood of Invariant Manifolds of Maps and Flows and Linearization (New York: Longman)
6. Bronstein I U and Kopanskii A Ya 1994 Smooth Invariant Manifolds and Normal Forms (Singapore: World Scientific)
7. Fenichel N 1971 Persistence and smoothness of invariant manifolds for flows Indiana Univ. Mathematics J. 2 193-226
8. Arnol'd V I, Afraimovich V S, Il'jashenko Yu S and Shil'nikov L P 1994 Bifurcation theory Dynamical Systems V, Encycl. Math. Sci. vol 5, ed V I Arnol'd (Berlin: Springer) pp 7-205
9. Ryashko L B 1996 The stability of stochastically perturbed orbital motions J. Appl. Math. Mech. 60 579-90
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11. Arnol'd V I 1993 Ordinary Differential Equations (Cambridge: MIT Press) 1973 (see also Arnol'd VI Ordinary Differential Equations (Berlin: Springer))
12. Anosov D V, Aranson S Kh, Bronshtein I U and Grinez V Z 1988 Smooth dynamical systems Dynamical Systems I, Encycl. Math. Sci. vol 1 (Berlin: Springer) pp 149-233
13. Arnol'd V I and Il'yashenko Yu S 1988 Ordinary differential equations Dynamical Systems I, Encycl. Math. Sci. vol 1 (Berlin: Springer) pp 1-148
14. Arnol'd VI 1983 Geometric Methods in the Theory of Ordinary Differential Equations (Berlin: Springer)