Difference of nonvanishing vector fields
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From: LordBeotian on 9 May 2010 11:37 Given two vector fields on R^2 V and W consider the vector field given by the difference V-W. If V and W are always nonzero can V-W have nontrivial periodic orbits?
From: Robert Israel on 9 May 2010 12:53
LordBeotian <pokipsy76(a)yahoo.it> writes: > Given two vector fields on R^2 V and W consider the vector field given > by the difference V-W. > If V and W are always nonzero can V-W have nontrivial periodic orbits? Hint: if F(x,y) = [F_1, F_2] is a vector field on R^2, then F + [F_1^2 + 1, 0] and [F_1^2 + 1, 0] are nonvanishing. -- Robert Israel israel(a)math.MyUniversitysInitials.ca Department of Mathematics http://www.math.ubc.ca/~israel University of British Columbia Vancouver, BC, Canada |