planar vector field conjugated with a constant field?

Discussion in 'Math Research' started by Pavel Pokorny, Jun 15, 2006.

  1. Dear math friends

    is it true that a planar continuous vector field with no equilibrium points
    is topologically conjugated with a constant nonzero field?

    This is my conjecture, most probably I have reinvented the wheel:)
    Is it possible to prove it?
    Or disprove?

    Thanks for any help
    Pavel Pokorny, Jun 15, 2006
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  2. No, take for example the vector field generating the following family
    of plane curves:
    exp(1/(1-x^2)) + c; x in (-1,1), c in R together with the straight
    lines x=a for |a|>=1.
    There is a topological classification of all such vector fields, I

    Best regards,
    Simeon Stefanov, Jun 19, 2006
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