Michel Henon - Böcker

hereafter calledvolume the of In a volume study previous (H6non 1997, I), the restricted initiated. families in problem (We generating three body was recallthat families defined asthe limits offamilies of are periodic generating determinationof orbitsfor Themain wasfoundto lieinthe 4 problem p 0.) bifurcation wheretwo the betweenthebranches ata ormore orbit, junctions A solutionto this was familiesof orbits intersect. partial problem generating and sidesof theuseofinvariants: Manysimple symmetries passage. givenby In the evolution of the bifurcations can be solved in this way. particular, orbits be described almost nine natural families of can completely. periodic become i.e.when thenumber of asthe bifurcations morecomplex, However, fails. the bifurcation orbit themethod families increases, passingthrough of This volume describes another to the a approach problem, consisting in of bifurcation ofthe families the a analysis vicinity detailed, quantitative used in Vol. I. orbit. This moreworkthan the requires qualitativeapproach in at to deter it has the of least, However, advantage allowing us, principle branches Infact it morethanthat: minein allcaseshowthe are joined. gives almost all the first order we will see in asymptotic approxima that, cases, the families in the ofthe bifurcation can be derived.tion of neighbourhood found in with This a comparison numerically allows, particular, quantitative families. and The 11 dealswiththerelevant definitions Chapter generalequations. of describedin 12 16.The ofbifurcations 1 is Chaps. study type quantitative it is described in 17 23. 3 of 2 ismore Chaps. Type analysis type involved; its hadnot been at thetime of isevenmore completed complex; analysis yet writing.

Thework described in this has somewhat erratically,over monograph grown, of than a more interest inthe was firstaroused period thirty My subject years. thebeautiful and inBroucke.'sthesis also by see computations drawings (1963; Broucke where familiesof orbits in the restricted three 1968), periodic body for the Earth Moon ratio = were mass problem investigated (/.I 0.012155). These that natural for the existence ofthe a explanation drawingssuggested observed familiesand for the found the of orbits could be shapes perhaps by to the limit + 0. a recourse y As first it a to as as step, appeared catalog completely possible necessary the orbits obtained in this limit. orbits of the first generaiing Generating hadbeen studied andother authors. Poincar6 specZes by (1892) Surprisingly, the two other had been Orbits ofthe however, species apparently neglected. second orbits with or consecutive a species, collisions, present comparatively the ofthe simple problem, only two body problem; no using equations yet had been done.An ofthe systematic ever constituent arcs study inventory was inH6non presented (1968).Also little work had been done on farmlies of orbits of the third very to Hill's A numerical species, was corresponding problem. investigation pub lished inR6non (1969).

Thework described in this has somewhat erratically,over monograph grown, of than a more interest inthe was firstaroused period thirty My subject years. thebeautiful and inBroucke.'sthesis also by see computations drawings (1963; Broucke where familiesof orbits in the restricted three 1968), periodic body for the Earth Moon ratio = were mass problem investigated (/.I 0.012155). These that natural for the existence ofthe a explanation drawingssuggested observed familiesand for the found the of orbits could be shapes perhaps by to the limit + 0. a recourse y As first it a to as as step, appeared catalog completely possible necessary the orbits obtained in this limit. orbits of the first generaiing Generating hadbeen studied andother authors. Poincar6 specZes by (1892) Surprisingly, the two other had been Orbits ofthe however, species apparently neglected. second orbits with or consecutive a species, collisions, present comparatively the ofthe simple problem, only two body problem; no using equations yet had been done.An ofthe systematic ever constituent arcs study inventory was inH6non presented (1968).Also little work had been done on farmlies of orbits of the third very to Hill's A numerical species, was corresponding problem. investigation pub lished inR6non (1969).