Invariant manifolds and Grobman-Hartman theorem for equations with degenerate operator at the derivative

Date

2003-01-01

Author

Karasözen, Bülent
Loginov, B

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Analog of Grobman-Hartman theorem about stable and unstable manifolds solutions for differential equations in Banach spaces with degenerate Fredholm operator at the derivative are proved. In contrast to usual evolution equation here central manifold arises even in the case of spectrum absence on the imaginary axis. Jordan chains tools and implicit operator theorem are used. The obtained results allow to develop center manifold methods for computation of bifurcation solution asymptotics and their stability investigation.

Subject Keywords

Invariant manifold, Imaginary axis, Stable manifold, Fredholm operator, Manifold theory

URI

https://hdl.handle.net/11511/54494

Journal

COMPUTATIONAL SCIENCE - ICCS 2003, PT II, PROCEEDINGS

Collections

Graduate School of Applied Mathematics, Article

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Citation Formats

B. Karasözen and B. Loginov, “Invariant manifolds and Grobman-Hartman theorem for equations with degenerate operator at the derivative,” COMPUTATIONAL SCIENCE - ICCS 2003, PT II, PROCEEDINGS, pp. 533–541, 2003, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/54494.