Scientific heritage of LP Shilnikov

被引：36

作者：

Afraimovich, Valentin S. ^{[1
]}

Gonchenko, Sergey V. ^{[2
]}

Lerman, Lev M. ^{[2
]}

Shilnikov, Andrey L. ^{[2
,3
,4
]}

Turaev, Dmitry V. ^{[5
]}

机构：

[1] Univ Autonoma San Luis Potosi, Av Karakorum 1470,Lomas 4a, San Luis Potosi 78210, Mexico

[2] Lobachevsky State Univ Nizhny Novgorod, Nizhnii Novgorod 603950, Russia

[3] Georgia State Univ, Neurosci Inst, Atlanta, GA 30303 USA

[4] Georgia State Univ, Dept Math & Stat, Atlanta, GA 30303 USA

[5] Univ London Imperial Coll Sci Technol & Med, London SW7 2AZ, England

来源：

REGULAR & CHAOTIC DYNAMICS | 2014年 / 19卷 / 04期

关键词：

Homoclinic chaos; global bifurcations; spiral chaos; strange attractor; saddle-focus; homoclinic loop; saddle-node; saddle-saddle; Lorenz attractor; hyperbolic set; SADDLE-FOCUS; HOMOCLINIC LOOPS; BIFURCATIONS; SYSTEMS; APPEARANCE; ATTRACTORS; DYNAMICS; ORBITS; CURVE; CHAOS;

D O I：

10.1134/S1560354714040017

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

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.

引用

页码：435 / 460

页数：26

共 116 条

[1]

Afraimovich V. S., 1988, Soviet Physics - Doklady, V33, P720

[2]

Afraimovich V. S., 1989, PMM-J APPL MATH MEC, V3, P24

[3]

Afraimovich V. S., 2014, REGUL CHAOT IN PRESS

[4]

Afraimovich V. S., 1980, RUSS MATH SURV, V35, P164

[5]

Afraimovich V. S., 1974, SOV MATH DOKL, V15, P734

[6]

Afraimovich V. S., 1974, MATH USSR IZV, V8, P1235

[7]

Afraimovich ValentinSendorovich., 1973, T MOSCOW MATH SOC, V28, P179

[8]

AFRAIMOVICH VS, 1977, DOKL AKAD NAUK SSSR+, V234, P336

[9]

AFRAIMOVICH VS, 1974, DOKL AKAD NAUK SSSR+, V219, P1281

[10]

Afraimovich VS., 1983, NONLINEAR DYNAMICS T, P1

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