Mathematics, 31.07.2021 04:00, papasully1

A smooth vector field on the phase plane is known to have exactly three closed orbits. Two of the cycles, say C1 and C2 , lie inside the third cycle C3 . However, C1 does not lie inside C2 , nor vice-versa. a) Sketch the arrangement of the three cycles. b) Show that there must be at least one fixed point in the region bounded by C1 ,C2 , C3 .

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A smooth vector field on the phase plane is known to have exactly three closed orbits. Two of the cy...