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Book Review
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Book Information
Author(s):
Oliver Knill
Title:
Jürgen Moser, selected chapters in the calculus of variations
Additional book information:
Birkhäuser Verlag,
Basel-Boston-Berlin,
2003,
iv+132 pp.,
EUR 25.68,
ISBN 3-7643-2185-7
References:
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- S. Aubry and P.Y. Le Daeron, The discrete Frenkel-Kontorova model and its extensions I: Exact results for the ground states, Physica 8D (1983), 381-422. MR 0719634 (85f:58032)
- [Ban1]
- V. Bangert, Minimal geodesics, Erg. Th. Dynam. Sys. 10 (1990), 263-286. MR 1062758 (91j:58126)
- [Ban2]
- V. Bangert, Existence of a complex line in tame almost complex tori, Duke Math. J. 94 (1998), 29-40. MR 1635896 (99j:58030)
- [BIK]
- D. Burago, S. Ivanov and B. Kleiner, On the structure of the stable norm of periodic metrics, Math. Res. Lett. 4 (1997), 791-808. MR 1492121 (98k:53051)
- [CL]
- L.A. Caffarelli and R. de la Llave, Planelike minimizers in periodic media, Comm. Pure Appl. Math. 54 (2001), 1403-1441. MR 1852978 (2002j:49003)
- [Fat]
- A. Fathi, Weak KAM Theorem and Lagrangian Dynamics, in preparation.
- [Gro]
- M. Gromov, Hyperbolic Groups, in: Essays in Group Theory (S. Gersten, ed.), MSRI Publications 8, pp. 75-265, Springer, 1987. MR 0919829 (89e:20070)
- [Hed]
- G.A. Hedlund, Geodesics on a two-dimensional Riemannian manifold with periodic coefficients, Ann. of Math. 33 (1932), 719-739. MR 1503086
- [Kli]
- W. Klingenberg, Geodätischer Fluss auf Mannigfaltigkeiten vom hyperbolischen Typ, Invent. Math. 14 (1971), 63-82. MR 0296975 (45:6034)
- [Mat1]
- J.N. Mather, Existence of quasi-periodic orbits for twist homeomorphisms of the annulus, Topology 21 (1982), 465-476. MR 0670747 (84g:58084)
- [Mat2]
- J.N. Mather, Variational construction of orbits of twist diffeomorphisms, J. Amer. Math. Soc. 4 (1991), 207-263. MR 1080112 (92d:58139)
- [Mat3]
- J.N. Mather, Action minimizing invariant measures for positive definite Lagrangian systems, Math. Z. 207 (1991), 169-207. MR 1109661 (92m:58048)
- [Mat4]
- J.N. Mather, Variational construction of connecting orbits, Ann. Inst. Fourier 43 (1993), 1349-1386. MR 1275203 (95c:58075)
- [Mat5]
- J.N. Mather, Arnold diffusion I: Announcement of results, preprint, 2002.
- [Mor]
- M. Morse, A fundamental class of geodesics on any closed surface of genus greater than one, Trans. Am. Math. Soc. 26 (1924), 25-60. MR 1501263
- [Mos1]
- J. Moser, Minimal solutions of variational problems on a torus, Ann. Inst. H. Poincaré - Anal. Non Linéaire 3 (1986), 229-272. MR 0847308 (88a:58058)
- [Mos2]
- J. Moser, On the persistence of pseudo-holomorphic curves on an almost complex torus (with an appendix by Jürgen Pöschel), Invent. Math. 119 (1995), 401-442. MR 1317647 (96a:58029)
- [RS]
- P. H. Rabinowitz and E. Stredulinsky, Mixed states for an Allen-Cahn type equation, Comm. Pure Appl. Math. 56 (2003), 1078-1134. MR 1989227 (2004i:35125)
- [Xia]
- Z. Xia, Arnold diffusion: a variational construction, Proc. Internat. Congr. Math. 1998, Vol. II, 867-877. MR 1648133 (99g:58112)
Additional Information:
Reviewer(s):
Victor
Bangert
Affiliation:
Mathematisches Institut der Universität Freiburg
Email:
bangert@email.mathematik.uni-freiburg.de
Review Information:
Journal:
Bull. Amer. Math. Soc.
42
(2005),
245-249.
MSC
(2000):
Primary 49-02, 37J50, 37E40, 53C22, 53D25
PII:
S 0273-0979(05)01044-X
Posted:
January 12, 2005
Copyright of article:
Copyright
2005,
American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.
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