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Topological equivalence

  1. Nov 1, 2012 #1
    It would be helpful if someone could please explain topological equivalence of functions in simple words?
    I am working on dynamical systems and chaos theory.In the underlying material,topological equivalence has taken a more complex definition involving orbits.Please be kind enough to explain this part also.
    'What does it mean for 2 maps to be topologically equivalent'?
    Thankyou.
     
  2. jcsd
  3. Nov 1, 2012 #2

    K41

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    The dynamics of one system A are topologically equivalent to the dynamics of another system B, if a homeomorphic function exists such that it can map from one vector A to the other vector B and preserve the direction of time.
     
  4. Nov 2, 2012 #3
    Is this the same definition of 'holomorphic function' we use in complex analysis?i.e A function f is holomorphic at a point z if it is C differentiable in a neighborhood of z/preserves angles and orientation in space.??Does preserving the direction of time also come into special consideration only for dynamical systems?

    Are the topological properties of a dynamical system the same as the properties of a topological space?

    What does it mean when one says the perturbed system is topologically isomorphic to the unpurturbed system?
     
    Last edited: Nov 2, 2012
  5. Nov 2, 2012 #4

    HallsofIvy

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    No one has mentioned "holomorphic". djpailo used the word "homeomorphic".

    A "homeomorphism" is an invertible, continuous, function from one topological space to another and two topological spaces are "equivalent" if and only if there exist a homeomophism from one to the other.
     
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