1) (Chicone Ex. 1.76) Prove that a gradient system cannot have a periodic orbit. 2) (Chicone...

 

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1) (Chicone Ex. 1.76) Prove that a gradient system cannot have a periodic orbit. 2) (Chicone Ex 1.201) Prove that the system i=r-y-r³, y=x+y=y³, x,y € R. has a unique periodic orbit that is globally attracting on R²\ {0}. (This means that, for any { € R², { 0, 0(t: §) converges to the periodic orbit.) 1) (Chicone Ex. 1.76) Prove that a gradient system cannot have a periodic orbit. 2) (Chicone Ex 1.201) Prove that the system i=r-y-r³, y=x+y=y³, x,y € R. has a unique periodic orbit that is globally attracting on R²\ {0}. (This means that, for any { € R², { 0, 0(t: §) converges to the periodic orbit.)