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Эта публикация цитируется в 36 научных статьях (всего в 37 статьях)
Scientific Heritage of L.P. Shilnikov
Valentin S. Afraimovicha, Sergey V. Gonchenkob, Lev M. Lermanb, Andrey L. Shilnikovbc, Dmitry V. Turaevd a Universidad Autónoma de San Luis Potosí, Av. Karakorum 1470, Lomas 4a. San Luis Potosí, 78210, México
b Lobachevsky State University of Nizhny Novgorod,
pr. Gagarina 23, Nizhny Novgorod, 603950 Russia
c Neuroscience Institute and Department of Mathematics and Statistics,
Georgia State University, Atlanta 30303, USA
d Imperial College, SW7 2 AZ London, UK
Аннотация:
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.
Ключевые слова:
Homoclinic chaos, global bifurcations, spiral chaos, strange attractor, saddle-focus, homoclinic loop, saddle-node, saddle-saddle, Lorenz attractor, hyperbolic set.
Поступила в редакцию: 01.07.2014 Принята в печать: 11.07.2014
Образец цитирования:
Valentin S. Afraimovich, Sergey V. Gonchenko, Lev M. Lerman, Andrey L. Shilnikov, Dmitry V. Turaev, “Scientific Heritage of L.P. Shilnikov”, Regul. Chaotic Dyn., 19:4 (2014), 435–460
Образцы ссылок на эту страницу:
https://www.mathnet.ru/rus/rcd164 https://www.mathnet.ru/rus/rcd/v19/i4/p435
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