PERIODIC ORBITS OF LAGRANGIAN SYSTEMS WITH PRESCRIBED ACTION OR PERIOD

被引：2

作者：

Paternain, Miguel ^{[1
]}

机构：

[1] Univ Republica, Fac Ciencias, Ctr Matemat, Igua 4225, Montevideo 11400, Uruguay

来源：

PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY | 2016年 / 144卷 / 07期

关键词：

Convex Lagrangian; action functional; periodic orbit; PALAIS-SMALE CONDITION; MANES CRITICAL-VALUES; FLOER HOMOLOGY; ENERGY; FLOWS;

D O I：

10.1090/proc/12950

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We show that for every convex Lagrangian quadratic at infinity there is a real number a(0) such that for every a > a(0) the Lagrangian has a periodic orbit with action a. We attain estimates on the period and energy of the periodic orbits obtained. We also show that such a Lagrangian has periodic orbits of every period.

引用

页码：2999 / 3007

页数：9

共 50 条

[1] PERIODIC ORBITS OF TONELLI LAGRANGIANS WITH PRESCRIBED ACTION OR PERIOD
Paternain, Miguel
[J]. PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 2023, : 209 - 222
[2] Linear instability of periodic orbits of free period Lagrangian systems
Portaluri, Alessandro
Wu, Li
Yang, Ran
[J]. ELECTRONIC RESEARCH ARCHIVE, 2022, 30 (08): : 2833 - 2859
[3] PERIODIC ORBITS WITH PRESCRIBED ABBREVIATED ACTION
Paternain, Miguel
[J]. PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 2015, 143 (09) : 4001 - 4008
[4] CONTRACTIBLE PERIODIC ORBITS OF LAGRANGIAN SYSTEMS
Paternain, Miguel
[J]. BULLETIN OF THE AUSTRALIAN MATHEMATICAL SOCIETY, 2019, 99 (03) : 445 - 453
[5] On the type of certain periodic orbits minimizing the Lagrangian action
Arnaud, MC
[J]. NONLINEARITY, 1998, 11 (01) : 143 - 150
[6] Relative periodic orbits of symmetric Lagrangian systems
Mccord, C
Montaldi, J
Roberts, M
Sbano, L
[J]. EQUADIFF 2003: INTERNATIONAL CONFERENCE ON DIFFERENTIAL EQUATIONS, 2005, : 482 - 493
[7] Connecting orbits for some classes of almost periodic Lagrangian systems
Bertotti, ML
Montecchiari, P
[J]. JOURNAL OF DIFFERENTIAL EQUATIONS, 1998, 145 (02) : 453 - 468
[8] Periodic orbits in magnetic fields and Ricci curvature of Lagrangian systems
Bahri, A
Taimanov, IA
[J]. TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 1998, 350 (07) : 2697 - 2717
[9] Detection of Periodic Orbits in Hamiltonian Systems Using Lagrangian Descriptors
Demian, Atanasiu Stefan
Wiggins, Stephen
[J]. INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS, 2017, 27 (14):
[10] Holomorphic cylinders with Lagrangian boundaries and periodic orbits of Hamiltonian systems
Gatien, D
[J]. TOPOLOGY AND ITS APPLICATIONS, 1998, 88 (1-2) : 147 - 154

← 1 2 3 4 5 →