Abstract:
We review the works initiated and developed by L.P. Shilnikov on homoclinic
chaos, highlighting his fundamental contributions to Poincaré homoclinics to periodic orbits
and invariant tori. Additionally, we discuss his related findings in non-autonomous and infinitedimensional
systems. This survey continues our earlier review [1], where we examined Shilnikov's
groundbreaking results on bifurcations of homoclinic orbits — his extension of the classical work
by A.A. Andronov and E.A. Leontovich from planar to multidimensional autonomous systems,
as well as his pioneering discoveries on saddle-focus loops and spiral chaos.
Keywords:saddle periodic orbit, Poincaré homoclinic orbit, hyperbolic set, symbolic dynamics,
nonautonomous system, integral curve, exponential dichotomy, Banach space
References