Scientific Heritage of L.P. Shilnikov. Part II. Homoclinic Chaos

We review the works initiated and developed by L.P. Shilnikov on homoclinic chaos, highlighting his fundamental contributions to Poincar´e 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.