planar vector field conjugated with a constant field?

Pavel Pokorny · science forum beginner Joined: 21 May 2005 Posts: 12

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
Math Dept, Prague Institute of Chemical Technology
http://www.vscht.cz/mat/Pavel.Pokorny

Simeon Stefanov · science forum beginner Joined: 09 Feb 2005 Posts: 13

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
suppose.

Best regards,
Simeon

Pavel Pokorny wrote:

Google