American Institute of Mathematical Sciences

Advanced
April  1997, 3(2): 189-205. doi: 10.3934/dcds.1997.3.189

Linearization near a locally nonunique invariant manifold

George Osipenko 1,

1. 

Department of Mathematics, State Technical University, St.Petersburg, 194044, Russian Federation

Received  September 1996 Published  January 1997

Theorem of C. Pugh and M. Shub states that a flow can be linearized near normally hyperbolic compact invariant manifold. A normally hyperbolic manifold has the property of local uniqueness. This paper gives conditions for linearization of a flow near an invariant manifold without the assumption of its local uniqueness. These conditions are wider than the normally hyperbolicity condition.
Keywords: Hyperbolic manifold, invariant manifold..
Mathematics Subject Classification: 34C30, 58F30, 39A1.
Citation: George Osipenko. Linearization near a locally nonunique invariant manifold. Discrete & Continuous Dynamical Systems - A, 1997, 3 (2) : 189-205. doi: 10.3934/dcds.1997.3.189
[1]

Awais Younus, Zoubia Dastgeer, Nudrat Ishaq, Abdul Ghaffar, Kottakkaran Sooppy Nisar, Devendra Kumar. On the observability of conformable linear time-invariant control systems. Discrete & Continuous Dynamical Systems - S, 2020  doi: 10.3934/dcdss.2020444
[2]

Gunther Uhlmann, Jian Zhai. Inverse problems for nonlinear hyperbolic equations. Discrete & Continuous Dynamical Systems - A, 2021, 41 (1) : 455-469. doi: 10.3934/dcds.2020380
[3]

Ilyasse Lamrani, Imad El Harraki, Ali Boutoulout, Fatima-Zahrae El Alaoui. Feedback stabilization of bilinear coupled hyperbolic systems. Discrete & Continuous Dynamical Systems - S, 2020  doi: 10.3934/dcdss.2020434
[4]

Mark F. Demers. Uniqueness and exponential mixing for the measure of maximal entropy for piecewise hyperbolic maps. Discrete & Continuous Dynamical Systems - A, 2021, 41 (1) : 217-256. doi: 10.3934/dcds.2020217
[5]

Antoine Benoit. Weak well-posedness of hyperbolic boundary value problems in a strip: when instabilities do not reflect the geometry. Communications on Pure & Applied Analysis, 2020, 19 (12) : 5475-5486. doi: 10.3934/cpaa.2020248

2019 Impact Factor: 1.338

Tools

Metrics

  • PDF downloads (33)
  • HTML views (0)
  • Cited by (4)

Other articles
by authors

[Back to Top]

Copyright © 2020 American Institute of Mathematical Sciences