Regular and chaotic motion in some quartic potentials
A Carnegie; I C Percival; A Carnegie; Dept. of Appl. Math., Queen Mary Coll., Univ. of London, London, UK; I C Percival; Dept. of Appl. Math., Queen Mary Coll., Univ. of London, London, UK
Журнал:
Journal of Physics A: Mathematical and General
Дата:
1984-03-11
Аннотация:
The Hamiltonian H<sub>alpha </sub>(x,y,p<sub>x</sub>,p<sub>y</sub>)=1/2(p<sub>x</sub><sup>2</sup>+p<sub>y</sub><sup>2</sup>)+V<sub>alpha </sub>(x,y) with O<or= alpha <or=1 and V<sub>alpha </sub>(x,y)=1/24((x+y)<sup>4</sup>+(x-y)<sup>4</sup>)-1/24( alpha (x<sup>4</sup>+y<sup>4</sup>)) is integrable for alpha =0, and for alpha =1 the potential is V<sub>1</sub>(x,y)=1/2(x<sup>2</sup>y<sup>2</sup>). A detailed numerical study using surfaces of section and properties of periodic orbits for the entire range of alpha strongly indicates that there are no invariants for H<sub>1</sub>, so the motion is completely chaotic. This result presents problems for the semiclassical quantisation of gauge fields.
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