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In the theory of dynamical systems, the Hartman–Grobman theorem states that there is a homeomorphism of a neighborhood which conjugates the original system and its linearization. A problem bothers me: is such a homeomorphism unique?

bifurcat
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1 Answers1

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Hint: there are homeomorphisms that take the linear system to itself.

Robert Israel
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  • If you are implying that they are (may) not be unique, then does it mean that the dissastifaction of the theorem does not nessesarily mean that the linear and nonlinear system do not behave similarly in the neighbourhood of the equilibrium point? – Zero Apr 05 '16 at 11:14
  • I am implying that the homeomorphism is never unique. This does not mean they don't behave similarly. – Robert Israel Apr 05 '16 at 15:15