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Dynamical System (timtam's question at Yahoo! Answers)

Fernando Revilla

Well-known member
MHB Math Helper
Jan 29, 2012
661

Fernando Revilla

Well-known member
MHB Math Helper
Jan 29, 2012
661
Hello timtam,

On $x^2+y^2=1$ we have $$(x,y)\cdot v(x,y)=(x,y)\cdot \left(-y -x\sqrt{x^2+y^2},x -y\sqrt{x^2+y^2}\right)=\ldots=-2<0$$ That is, on the boundary of the closed set $R\equiv x^2+y^2\le 1$ the vector field is pointing towards the interior of $R$ so, the open unit disk is a trapping region.