Re: dynamical systems in R^2

Thank you to Prof. Israel and Prof. Nordhaus for the valuable
information.

Greg Spradlin

On Oct 24, 5:12 pm, Robert Israel
<isr...@xxxxxxxxxxxxxxxxxxxxxxxxxxxxx> wrote:
sprad...@xxxxxxxx writes:
I have a question. Let f be a smooth vector field on R^2 and consider
the dynamical system x' = f(x), x:R->R^2. Suppose w(t) is a bounded
orbit of the dynamical system. I would like to assert that the limit
points of w(t) as t goes to infinity, that is, the omega-set of w, is
a fixed point of f or form a periodic orbit. Is this true, and can
anyone suggest a reference?

No, it's not true. It could also be a homoclinic orbit plus a fixed point,
or a heteroclinic cycle.
--
Robert Israel isr...@xxxxxxxxxxxxxxxxxxxxxxxxxxxxx
Department of Mathematics http://www.math.ubc.ca/~israel
University of British Columbia Vancouver, BC, Canada


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