Scientific Heritage of L.P. Shilnikov

    2014, Volume 19, Number 4, pp.  435-460

    Author(s): Afraimovich V. S., Gonchenko S. V., Lerman L. M., Shilnikov A. L., Turaev D. V.

    This is the first part of a review of the scientific works of L.P. Shilnikov. We group his papers according to 7 major research topics: bifurcations of homoclinic loops; the loop of a saddle-focus and spiral chaos; Poincare homoclinics to periodic orbits and invariant tori, homoclinic in noautonous and infinite-dimensional systems; Homoclinic tangency; Saddlenode bifurcation — quasiperiodicity-to-chaos transition, blue-sky catastrophe; Lorenz attractor; Hamiltonian dynamics. The first two topics are covered in this part. The review will be continued in the further issues of the journal.
    Keywords: Homoclinic chaos, global bifurcations, spiral chaos, strange attractor, saddle-focus, homoclinic loop, saddle-node, saddle-saddle, Lorenz attractor, hyperbolic set
    Citation: Afraimovich V. S., Gonchenko S. V., Lerman L. M., Shilnikov A. L., Turaev D. V., Scientific Heritage of L.P. Shilnikov, Regular and Chaotic Dynamics, 2014, Volume 19, Number 4, pp. 435-460

    Access to the full text on the Springer website