On periodic orbits in cotangent bundles of non-compact manifolds

被引：8

作者：

van den Berg, J. B. ^{[1
]}

Pasquotto, F. ^{[1
]}

Rot, T. ^{[1
]}

Vandervorst, R. C. A. M. ^{[1
]}

机构：

[1] Vrije Univ Amsterdam, Dept Math, Boelelaan 1081A, NL-1081 HV Amsterdam, Netherlands

来源：

JOURNAL OF SYMPLECTIC GEOMETRY | 2016年 / 14卷 / 04期

关键词：

Periodic orbits; Weinstein conjecture; Hamiltonian dynamics; free loop space; linking sets; HAMILTONIAN-SYSTEMS; PRESCRIBED ENERGY;

D O I：

10.4310/JSG.2016.v14.n4.a6

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

This paper is concerned with the existence of periodic orbits on energy hypersurfaces in cotangent bundles of Riemannian manifolds defined by mechanical Hamiltonians. In [14] it was proved that, provided certain geometric assumptions are satisfied, regular mechanical hypersurfaces in R-2n, in particular non-compact ones, contain periodic orbits if one homology group among the top half does not vanish. In the present paper we extend the above mentioned existence result to a class of hypersurfaces in cotangent bundles of Riemannian manifolds with fiat ends.

引用

页码：1145 / 1173

页数：29

共 19 条

[1]

BENCI V, 1984, ANN I H POINCARE-AN, V1, P401

[2]

Bolotin S. V., 1978, VESTNIK MOSKOVSKOGO, V1, P72

[3]

Frauenfelder U., 2005, PREPUBLICATION ORSAY, V387, P129

[4]

Gluck H., 1983, SEMINAR MINIMAL SUBM, P65

[5]

Hofer H., 1989, ANN SCUOLA NORM-SCI, V15, P411

[6]

Klingenberg W., 1978, Grundlehren der Mathematischen Wissenschaften

[7]

Klingenberg W. P., 1995, De Gruyter Studies in Mathematics, V1

[8]

Munkres J. R., 1975, Topology: A first course

[9]

Palais RS., 1963, TOPOLOGY, V2, P299, DOI DOI 10.1016/0040-9383(63)90013-2

[10]

RABINOWITZ PH, 1978, COMMUN PUR APPL MATH, V31, P31

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