Abstract
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.
| Original language | English |
|---|---|
| Pages (from-to) | 435-460 |
| Number of pages | 26 |
| Journal | Regular and Chaotic Dynamics |
| Volume | 19 |
| Issue number | 4 |
| DOIs | |
| State | Published - 1 Jan 2014 |
| Externally published | Yes |
Keywords
- Global bifurcations
- Homoclinic chaos
- Homoclinic loop
- Hyperbolic set
- Lorenz attractor
- Saddle-focus
- Saddle-node
- Saddle-saddle
- Spiral chaos
- Strange attractor
ASJC Scopus subject areas
- Statistical and Nonlinear Physics
- Mathematics (miscellaneous)
- Modeling and Simulation
- Mathematical Physics
- Mechanical Engineering
- Applied Mathematics
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