▁variables . ▁ ▁Background ▁and ▁statement ▁For ▁integra ble ▁systems , ▁one ▁has ▁the ▁conservation ▁of ▁the ▁action ▁variables . ▁ ▁According ▁to ▁the ▁K AM ▁theorem ▁if ▁we ▁perturb ▁an ▁integra ble ▁system ▁slightly , ▁then ▁many , ▁though ▁certainly ▁not ▁all , ▁of ▁the ▁solutions ▁of ▁the ▁pert urbed ▁system ▁stay ▁close , ▁for ▁all ▁time , ▁to ▁the ▁un pert urbed ▁system . ▁ ▁In ▁particular , ▁since ▁the ▁action ▁variables ▁were ▁originally ▁conser ved , ▁the ▁ ▁theorem ▁tells ▁us ▁that ▁there ▁is ▁only ▁a ▁small ▁change ▁in ▁action ▁for ▁many ▁solutions ▁of ▁the ▁pert urbed ▁system . ▁▁▁ ▁However , ▁as ▁first ▁noted ▁in ▁Arnold ' s ▁paper , ▁there ▁are ▁nearly ▁integra ble ▁systems ▁for ▁which ▁there ▁exist ▁solutions ▁that ▁exhib it ▁arbitr arily ▁large ▁growth ▁in ▁the ▁action ▁variables . ▁ ▁More ▁precisely , ▁Arnold ▁considered ▁the ▁example ▁of ▁nearly ▁integra ble ▁Hamiltonian ▁system ▁with ▁Hamiltonian ▁▁▁▁ ▁He ▁showed ▁that ▁for ▁this ▁system , ▁with ▁any ▁choice ▁of ▁ ▁where ▁, ▁there ▁exists ▁a ▁ ▁such ▁that ▁for ▁all ▁ ▁there ▁is ▁a ▁solution ▁to ▁the ▁system ▁for ▁which ▁▁▁▁ ▁for ▁some ▁time ▁ ▁See ▁also ▁K AM ▁theorem ▁N ek hor os he v ▁estimates ▁ ▁References ▁ ▁Category : D ynam ical ▁systems ▁Category : Class ical ▁mechan ics <0x0A> </s> ▁Rad ivo je ▁Ž iv k ović ▁( ; ▁born ▁ 1 1 ▁October ▁ 1 9 5 0 ), ▁sometimes ▁also ▁Rad iv oj , ▁is ▁a ▁retired ▁Ser bian ▁professional ▁basketball