Pseudoholomorphic curves and the shadowing lemma

previous :: next

Pseudoholomorphic curves and the shadowing lemma

Kai Cieliebak and Eric Séré

Source: Duke Math. J. Volume 99, Number 1 (1999), 41-73.

First Page: Show

Primary Subjects: 37J45

Secondary Subjects: 34C37, 37C29, 37D05, 37D45, 53D40, 58E05

Full-text: Access denied (no subscription detected)

We're sorry, but we are unable to provide you with the full text of this article because we are not able to identify you as a subscriber.

If you have a personal subscription to this journal, then please login. If you are already logged in, then you may need to update your profile to register your subscription. Read more about accessing full-text

Links and Identifiers

Permanent link to this document: http://projecteuclid.org/euclid.dmj/1077227630
Mathematical Reviews number (MathSciNet): MR1700739
Zentralblatt MATH identifier: 0955.37039
Digital Object Identifier: doi:10.1215/S0012-7094-99-09902-7

back to Table of Contents

References

[1] Vieri Benci and Fabio Giannoni, Homoclinic orbits on compact manifolds, J. Math. Anal. Appl. 157 (1991), no. 2, 568–576.

Mathematical Reviews (MathSciNet): MR92h:58150

Zentralblatt MATH: 0737.58052

Digital Object Identifier: doi:10.1016/0022-247X(91)90107-B

[2] Ugo Bessi, A variational proof of a Sitnikov-like theorem, Nonlinear Anal. 20 (1993), no. 11, 1303–1318.

Mathematical Reviews (MathSciNet): MR94e:58020

Zentralblatt MATH: 0778.34036

[3] S. V. Bolotin, Libration motions of natural dynamical systems, Vestnik Moskov. Univ. Ser. I Mat. Mekh. (1978), no. 6, 72–77, (in Russian), English translation in Moscow Univ. Mech. Bull. 33, no. 6 (1978), 49–53.

Mathematical Reviews (MathSciNet): MR80d:70021

Zentralblatt MATH: 0403.34053

[4] B. Buffoni and E. Séré, A global condition for quasi-random behavior in a class of conservative systems, Comm. Pure Appl. Math. 49 (1996), no. 3, 285–305.

Mathematical Reviews (MathSciNet): MR97g:58033

Zentralblatt MATH: 0860.58027

Digital Object Identifier: doi:10.1002/(SICI)1097-0312(199603)49:3<285::AID-CPA3>3.0.CO;2-9

[5] K. Cieliebak, Pseudo-holomorphic curves and periodic orbits on cotangent bundles, J. Math. Pures Appl. (9) 73 (1994), no. 3, 251–278.

Mathematical Reviews (MathSciNet): MR95g:58078

Zentralblatt MATH: 0837.58010

[6] Kai Cieliebak and Éric Séré, Pseudoholomorphic curves and multiplicity of homoclinic orbits, Duke Math. J. 77 (1995), no. 2, 483–518.

Mathematical Reviews (MathSciNet): MR95m:58025

Zentralblatt MATH: 0842.58022

Digital Object Identifier: doi:10.1215/S0012-7094-95-07715-1

Project Euclid: euclid.dmj/1077286350

[7] Vittorio Coti Zelati, Ivar Ekeland, and Éric Séré, A variational approach to homoclinic orbits in Hamiltonian systems, Math. Ann. 288 (1990), no. 1, 133–160.

Mathematical Reviews (MathSciNet): MR91g:58065

Zentralblatt MATH: 0731.34050

Digital Object Identifier: doi:10.1007/BF01444526

[8] Vittorio Coti Zelati and Paul H. Rabinowitz, Homoclinic orbits for second order Hamiltonian systems possessing superquadratic potentials, J. Amer. Math. Soc. 4 (1991), no. 4, 693–727.

Mathematical Reviews (MathSciNet): MR93e:58023

Zentralblatt MATH: 0744.34045

Digital Object Identifier: doi:10.2307/2939286

JSTOR: links.jstor.org

[9] Vittorio Coti Zelati and Paul H. Rabinowitz, Multibump periodic solutions of a family of Hamiltonian systems, Topol. Methods Nonlinear Anal. 4 (1994), no. 1, 31–57.

Mathematical Reviews (MathSciNet): MR96a:58042

Zentralblatt MATH: 0819.34028

[10] P. L. Felmer, Heteroclinic orbits for spatially periodic Hamiltonian systems, Ann. Inst. H. Poincaré Anal. Non Linéaire 8 (1991), no. 5, 477–497.

Mathematical Reviews (MathSciNet): MR93d:58024

Zentralblatt MATH: 0749.58021

[11] Andreas Floer, The unregularized gradient flow of the symplectic action, Comm. Pure Appl. Math. 41 (1988), no. 6, 775–813.

Mathematical Reviews (MathSciNet): MR89g:58065

Zentralblatt MATH: 0633.53058

Digital Object Identifier: doi:10.1002/cpa.3160410603

[12] Fabio Giannoni and Paul H. Rabinowitz, On the multiplicity of homoclinic orbits on Riemannian manifolds for a class of second order Hamiltonian systems, NoDEA Nonlinear Differential Equations Appl. 1 (1994), no. 1, 1–46.

Mathematical Reviews (MathSciNet): MR95c:58037

Zentralblatt MATH: 0823.34050

Digital Object Identifier: doi:10.1007/BF01194038

[13] M. Gromov, Pseudoholomorphic curves in symplectic manifolds, Invent. Math. 82 (1985), no. 2, 307–347.

Mathematical Reviews (MathSciNet): MR87j:53053

Zentralblatt MATH: 0592.53025

Digital Object Identifier: doi:10.1007/BF01388806

[14] H. Hofer, Lusternik-Schnirelman-theory for Lagrangian intersections, Ann. Inst. H. Poincaré Anal. Non Linéaire 5 (1988), no. 5, 465–499.

Mathematical Reviews (MathSciNet): MR91b:58068

Zentralblatt MATH: 0669.58006

[15] H. Hofer and K. Wysocki, First order elliptic systems and the existence of homoclinic orbits in Hamiltonian systems, Math. Ann. 288 (1990), no. 3, 483–503.

Mathematical Reviews (MathSciNet): MR91m:58064

Zentralblatt MATH: 0702.34039

Digital Object Identifier: doi:10.1007/BF01444543

[16]¹ P.-L. Lions, The concentration-compactness principle in the calculus of variations. The locally compact case. I, Ann. Inst. H. Poincaré Anal. Non Linéaire 1 (1984), no. 2, 109–145.

Mathematical Reviews (MathSciNet): MR87e:49035a

Zentralblatt MATH: 0541.49009

[16]² P.-L. Lions, The concentration-compactness principle in the calculus of variations. The locally compact case. II, Ann. Inst. H. Poincaré Anal. Non Linéaire 1 (1984), no. 4, 223–283.

Mathematical Reviews (MathSciNet): MR87e:49035b

Zentralblatt MATH: 0704.49004

[17] P. Montechiarri, M. Nolasco, and S. Terracini, A global condition for multibump phenomena in Duffing-like equations, to appear in Trans. Amer. Math. Soc.

[18] Jürgen Moser, Stable and random motions in dynamical systems, Princeton University Press, Princeton, N. J., 1973, Ann. Math. Stud. 77.

Mathematical Reviews (MathSciNet): MR56:1355

Zentralblatt MATH: 0271.70009

[19] H. Poincaré, Les méthodes nouvelles de la mécanique céleste, Vol. III, Gauthier-Villars, Paris, 1899.

Zentralblatt MATH: 30.0834.08

[20] Paul H. Rabinowitz, Periodic and heteroclinic orbits for a periodic Hamiltonian system, Ann. Inst. H. Poincaré Anal. Non Linéaire 6 (1989), no. 5, 331–346.

Mathematical Reviews (MathSciNet): MR91c:58117

Zentralblatt MATH: 0701.58023

[21] Paul H. Rabinowitz, A multibump construction in a degenerate setting, Calc. Var. Partial Differential Equations 5 (1997), no. 2, 159–182.

Mathematical Reviews (MathSciNet): MR98b:58034

Zentralblatt MATH: 0876.34055

Digital Object Identifier: doi:10.1007/s005260050064

[22] Éric Séré, Existence of infinitely many homoclinic orbits in Hamiltonian systems, Math. Z. 209 (1992), no. 1, 27–42.

Mathematical Reviews (MathSciNet): MR92k:58201

Zentralblatt MATH: 0725.58017

Digital Object Identifier: doi:10.1007/BF02570817

[23] Éric Séré, Looking for the Bernoulli shift, Ann. Inst. H. Poincaré Anal. Non Linéaire 10 (1993), no. 5, 561–590.

Mathematical Reviews (MathSciNet): MR95b:58031

Zentralblatt MATH: 0803.58013

[24] S. Smale, An infinite dimensional version of Sard's theorem, Amer. J. Math. 87 (1965), 861–866.

Mathematical Reviews (MathSciNet): MR32:3067

Zentralblatt MATH: 0143.35301

Digital Object Identifier: doi:10.2307/2373250

JSTOR: links.jstor.org

[25] Edwin H. Spanier, Algebraic topology, McGraw-Hill Book Co., New York, 1966.

Mathematical Reviews (MathSciNet): MR35:1007

Zentralblatt MATH: 0145.43303

[26] D. Sullivan, Differential forms and the topology of manifolds, Manifolds—Tokyo 1973 (Proc. Internat. Conf., Tokyo, 1973), Univ. Tokyo Press, Tokyo, 1975, and Related Topics in Topology, pp. 37–49.

Mathematical Reviews (MathSciNet): MR51:6838

Zentralblatt MATH: 0319.58005

[27] W. P. Thurston, Travaux de Thurston sur les surfaces, Astérisque, vol. 66, Société Mathématique de France, Paris, 1979, Séminaire Orsay.

Mathematical Reviews (MathSciNet): MR82m:57003

Zentralblatt MATH: 0406.00016

previous :: next

Duke Mathematical Journal

Turn MathJax Off
What is MathJax?