Scientific heritage of LP Shilnikov

被引：34
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.
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收藏
页码：435 / 460
页数：26
相关论文
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  • [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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