The Brouwer’s plane translation theorem asserts that for a fixed point free orientation preserving homeomorphism
@article{PMIHES_2005__102__1_0, author = {Le Calvez, Patrice}, title = {Une version feuillet\'ee \'equivariante du th\'eor\`eme de translation de {Brouwer}}, journal = {Publications Math\'ematiques de l'IH\'ES}, pages = {1--98}, publisher = {Springer}, volume = {102}, year = {2005}, doi = {10.1007/s10240-005-0034-1}, mrnumber = {2217051}, zbl = {1152.37015}, language = {fr}, url = {http://www.numdam.org/articles/10.1007/s10240-005-0034-1/} }
TY - JOUR AU - Le Calvez, Patrice TI - Une version feuilletée équivariante du théorème de translation de Brouwer JO - Publications Mathématiques de l'IHÉS PY - 2005 SP - 1 EP - 98 VL - 102 PB - Springer UR - http://www.numdam.org/articles/10.1007/s10240-005-0034-1/ DO - 10.1007/s10240-005-0034-1 LA - fr ID - PMIHES_2005__102__1_0 ER -
%0 Journal Article %A Le Calvez, Patrice %T Une version feuilletée équivariante du théorème de translation de Brouwer %J Publications Mathématiques de l'IHÉS %D 2005 %P 1-98 %V 102 %I Springer %U http://www.numdam.org/articles/10.1007/s10240-005-0034-1/ %R 10.1007/s10240-005-0034-1 %G fr %F PMIHES_2005__102__1_0
Le Calvez, Patrice. Une version feuilletée équivariante du théorème de translation de Brouwer. Publications Mathématiques de l'IHÉS, Tome 102 (2005), pp. 1-98. doi : 10.1007/s10240-005-0034-1. http://www.numdam.org/articles/10.1007/s10240-005-0034-1/
1. An extension of Poincaré's last geometric theorem, Acta Math., 47 (1925), 297-311. | JFM
,2. Beweis des ebenen Translationssatzes, Math. Ann., 72 (1912), 37-54. | JFM | MR
,3. A new proof of Brouwer's lemma on translation arcs, Houston J. Math., 10 (1984), 35-41. | Zbl
,4. An orientation preserving fixed point free homeomorphism of the plane which admits no closed invariant line, Topol. Appl., 29 (1988), 213-217. | MR | Zbl
, , and ,5. An improvment of the Poincaré-Birkhoff theorem, Trans. Am. Math. Soc., 269 (1982), 285-299. | MR | Zbl
,6. Isolated invariants sets and Morse index, CBMS Reg. Conf. Series in Math., Am. Math. Soc., 38 (1978). | MR | Zbl
,7. An orbit closing proof of Brouwer's lemma on translation arcs, Enseign. Math., 33 (1987), 315-322. | Zbl
,8. Proof of the Arnold conjectures for surfaces and generalizations to certain Kähler manifolds, Duke Math. J., 51 (1986), 1-32. | MR | Zbl
,9. Fixed points of measure preserving torus homeomorphism, Manuscr. Math., 68 (1990), 271-293. | MR | Zbl
,10. Generalizations of the Poincaré-Birkhoff theorem, Ann. Math., 128 (1988), 139-151. | MR | Zbl
,11. Recurrence and fixed points of surface homeomorphisms, Ergodic Theory Dyn. Syst., 8* (1988), 99-107. | MR | Zbl
,12. A new proof of the Brouwer plane translation theorem, Ergodic Theory Dyn. Syst., 12 (1992), 217-226. | MR | Zbl
,13. Geodesics on S2 and periodic points of annulus homeomorphisms, Invent. Math., 108 (1992), 403-418. | MR | Zbl
,14. Area preserving homeomorphisms of open surfaces of genus zero, New York J. Math., 2 (1996), 1-19. | MR | Zbl
,15. The Conley index and non-existence of minimal homeomorphisms, Ill. J. Maths, 43 (1999), 457-464. | MR | Zbl
,16. Periodic points of Hamiltonian surface diffeomorphims, Geom. Topol., 7 (2003), 713-756. | MR | Zbl
and ,17. J.-M. Gambaudo et P. Le Calvez, Infinité d'orbites périodiques pour les difféomorphismes conservatifs de l'anneau, Mém. Soc. Math Fr., 79 (1999), 125-146.
18. Théorème de translation plane de Brouwer et généralisations du théorème de Poincaré-Birkhoff, Topology, 33 (1994), 331-351. | MR | Zbl
,19. The space of homeomorphisms on a torus, Ill. J. Math., 9 (1965), 59-65. | MR | Zbl
,20. Homotopy groups of the space of homeomorphisms on a 2-manifold, Ill. J. Math., 10 (1966), 563-573. | MR | Zbl
,21. There are no minimal homeomorphisms of the multipunctured plane, Ergodic Theory Dyn. Syst., 12 (1992), 75-83. | MR | Zbl
,22. A fixed point theorem for planar homeomorphisms, Topology, 38 (1999), 235-264. | MR | Zbl
,23. New proofs of some results of Nielsen, Adv. Math., 56 (1985), 173-191. | MR | Zbl
and ,24. Symplectic invariants and Hamiltonian dynamics, Birkhäuser, Basel-Boston-Berlin (1994). | MR | Zbl
and ,25. The plane translation theorem of Brouwer and the last geometric theorem of Poincaré, Acta Sci. Math. Szeged, 4 (1928-29), 86-102. | JFM
,26. Lectures on Nielsen Fixed Point Theory, Contemp. Math., 14 (1983). | MR | Zbl
,27. Propriétés dynamiques de l'anneau et du tore, Astérisque, 204 (1991). | Numdam | Zbl
,28. Une généralisation du théorème de Conley-Zehnder aux homéomorphismes du tore de dimension deux, Ergodic Theory Dyn. Syst., 17 (1997), 71-86. | MR | Zbl
,29. Une propriété dynamique des homéomorphismes du plan au voisinage d'un point fixe d'indice > 1, Topology, 38 (1999), 25-35. | Zbl
,30. Dynamique des homéomorphismes du plan au voisinage d'un point fixe, Ann. Sci. Éc. Norm. Supér., IV Sér., 36 (2003), 139-171. | Numdam | Zbl
,31. Une version feuilletée du théorème de translation de Brouwer, Comment. Math. Helv., 21 (2004), 229-259. | MR | Zbl
,32. Une démonstration dynamique du théorème de translation de Brouwer, Expo. Math., 14 (1996), 277-287. | MR | Zbl
et ,33. P. Le Calvez et J.-C. Yoccoz, Suite des indices de Lefschetz des itérés pour un domaine de Jordan qui est un bloc isolant. Manuscrit.
34. Homéomorphismes de surfaces, théorème de la fleur de Leau-Fatou et de la variété stable, Astérisque, 292 (2004). | Numdam | MR | Zbl
,35. Arnold conjecture for surface homeomorphisms, Proceedings of the French-Japanese Conference “Hyperspace Topologies and Applications” (La Bussière, 1997), Topol. Appl., 104 (2000), 191-214. | Zbl
,36. Fixed points of diffeomorphisms of two-dimensional spheres preserving an oriented plane, Funkts. Anal. Prilozh., 8 (1974), 84-85. | MR | Zbl
,37. A bound for the fixed point index of area-preserving homeomorphisms of two-manifolds, Ergodic Theory Dyn. Syst., 7 (1987), 463-479. | MR | Zbl
and ,38. Morse theory for periodic solutions of Hamiltonian systems and the Maslov index, Commun. Pure Appl. Math., 45 (1992), 1303-1360. | MR | Zbl
and ,39. A. Sauzet, Application des décompositions libres à l'étude des homéomorphismes de surface, Thèse de l'Université Paris 13 (2001).
40. On the action spectrum for closed symplectically aspherical manifolds, Pac. J. Math., 193 (2000), 419-461. | MR | Zbl
,41. Asymptotic cycles, Ann. Math., 68 (1957), 270-284. | MR | Zbl
,42. Points fixes d'une application symplectique homologue à l'identité, J. Differ. Geom., 22 (1985), 49-79. | Zbl
,43. A bound for the fixed-point index of an area-preserving map with applications to mechanics, Invent. Math., 26 (1974), 187-200. | MR | Zbl
,- Quasi-intermediate value theorem and outflanking arc theorem for plane maps, Discrete and Continuous Dynamical Systems, Volume 0 (2024) no. 0, p. 0 | DOI:10.3934/dcds.2024162
- Hamiltonian Floer theory on surfaces: linking, positively transverse foliations and spectral invariants, Inventiones Mathematicae, Volume 237 (2024) no. 3, pp. 1377-1468 | DOI:10.1007/s00222-024-01274-0 | Zbl:7895066
- On non-contractible periodic orbits and bounded deviations, Nonlinearity, Volume 37 (2024) no. 7, p. 26 (Id/No 075007) | DOI:10.1088/1361-6544/ad4948 | Zbl:7867510
- Hofer's geometry and topological entropy, Compositio Mathematica, Volume 159 (2023) no. 6, pp. 1250-1299 | DOI:10.1112/s0010437x23007169 | Zbl:1527.37044
- On the existence of supporting broken book decompositions for contact forms in dimension 3, Inventiones Mathematicae, Volume 231 (2023) no. 3, pp. 1489-1539 | DOI:10.1007/s00222-022-01160-7 | Zbl:1512.53098
- The growth of the number of periodic orbits for annulus homeomorphisms and non-contractible closed geodesics on Riemannian or Finsler
, Journal of Differential Equations, Volume 357 (2023), pp. 362-387 | DOI:10.1016/j.jde.2023.02.012 | Zbl:1518.37037 - Transitivity and the existence of horseshoes on the 2-torus, Nonlinearity, Volume 36 (2023) no. 1, pp. 199-230 | DOI:10.1088/1361-6544/aca252 | Zbl:1509.37044
- Topological horseshoes for surface homeomorphisms, Duke Mathematical Journal, Volume 171 (2022) no. 12, pp. 2519-2626 | DOI:10.1215/00127094-2022-0057 | Zbl:1518.37054
- Homoclinic orbits for area preserving diffeomorphisms of surfaces, Ergodic Theory and Dynamical Systems, Volume 42 (2022) no. 3, pp. 1122-1165 | DOI:10.1017/etds.2021.40 | Zbl:1494.37025
- Non-existence of sublinear diffusion for a class of torus homeomorphisms, Ergodic Theory and Dynamical Systems, Volume 42 (2022) no. 4, pp. 1517-1547 | DOI:10.1017/etds.2020.137 | Zbl:1493.37052
- Quantitative Heegaard Floer cohomology and the Calabi invariant, Forum of Mathematics, Pi, Volume 10 (2022), p. 59 (Id/No e27) | DOI:10.1017/fmp.2022.18 | Zbl:1508.53090
- Refinements of Franks' theorem and applications in Reeb dynamics, Journal of Differential Equations, Volume 338 (2022), pp. 372-387 | DOI:10.1016/j.jde.2022.07.048 | Zbl:1505.37056
- Conservative surface homeomorphisms with finitely many periodic points, Journal of Fixed Point Theory and Applications, Volume 24 (2022) no. 2, p. 36 (Id/No 20) | DOI:10.1007/s11784-022-00936-x | Zbl:1535.37052
- Conservative surface homeomorphisms with finitely many periodic points, Symplectic geometry. A festschrift in honour of Claude Viterbo's 60th birthday. In 2 volumes, Cham: Birkhäuser, 2022, pp. 827-862 | DOI:10.1007/978-3-031-19111-4_28 | Zbl:7910430
- On the onset of diffusion in the kicked Harper model, Communications in Mathematical Physics, Volume 383 (2021) no. 2, pp. 953-980 | DOI:10.1007/s00220-021-03995-2 | Zbl:1466.37050
- Barcodes and area-preserving homeomorphisms, Geometry Topology, Volume 25 (2021) no. 6, pp. 2713-2825 | DOI:10.2140/gt.2021.25.2713 | Zbl:1494.37040
- The action spectrum and
symplectic topology, Mathematische Annalen, Volume 380 (2021) no. 1-2, pp. 293-316 | DOI:10.1007/s00208-021-02183-w | Zbl:1471.53067 - Dynamical systems. Abstracts from the workshop held July 11–17, 2021 (hybrid meeting), Oberwolfach Rep. 18, No. 3, 1735-1803, 2021 | DOI:10.4171/owr/2021/33 | Zbl:1506.00038
- Some results of Hamiltonian homeomorphisms on closed aspherical surfaces, Advances in Mathematics, Volume 373 (2020), p. 46 (Id/No 107307) | DOI:10.1016/j.aim.2020.107307 | Zbl:1453.37037
- Fixed point sets of isotopies on surfaces, Journal of the European Mathematical Society (JEMS), Volume 22 (2020) no. 6, pp. 1971-2046 | DOI:10.4171/jems/960 | Zbl:1442.37058
- Existence of non-contractible periodic orbits for homeomorphisms of the open annulus, Mathematische Zeitschrift, Volume 294 (2020) no. 3-4, pp. 1413-1439 | DOI:10.1007/s00209-019-02309-6 | Zbl:1439.37046
- A triple boundary lemma for surface homeomorphisms, Proceedings of the American Mathematical Society, Volume 147 (2019) no. 2, pp. 681-686 | DOI:10.1090/proc/14258 | Zbl:1435.37066
- Existence of torsion-low maximal isotopies for area preserving surface homeomorphisms, Discrete and Continuous Dynamical Systems, Volume 38 (2018) no. 9, pp. 4571-4602 | DOI:10.3934/dcds.2018200 | Zbl:1396.37052
- Fully essential dynamics for area-preserving surface homeomorphisms, Ergodic Theory and Dynamical Systems, Volume 38 (2016) no. 5, pp. 1791-1836 | DOI:10.1017/etds.2016.110 | Zbl:1404.37045
- The local rotation set is an interval, Ergodic Theory and Dynamical Systems, Volume 38 (2018) no. 7, pp. 2571-2617 | DOI:10.1017/etds.2016.129 | Zbl:1402.37055
- Rotation intervals and entropy on attracting annular continua, Geometry Topology, Volume 22 (2018) no. 4, pp. 2145-2186 | DOI:10.2140/gt.2018.22.2145 | Zbl:1386.37042
- Forcing theory for transverse trajectories of surface homeomorphisms, Inventiones Mathematicae, Volume 212 (2018) no. 2, pp. 619-729 | DOI:10.1007/s00222-017-0773-x | Zbl:1390.37073
- A
counterexample to the Arnold conjecture, Inventiones Mathematicae, Volume 213 (2018) no. 2, pp. 759-809 | DOI:10.1007/s00222-018-0797-x | Zbl:1395.37037 - On annular maps of the torus and sublinear diffusion, Journal of the Institute of Mathematics of Jussieu, Volume 17 (2018) no. 4, pp. 913-978 | DOI:10.1017/s1474748016000268 | Zbl:1396.37051
- Generalizations of the action function in symplectic geometry, Annales Henri Poincaré, Volume 18 (2017) no. 9, pp. 2945-2993 | DOI:10.1007/s00023-017-0596-8 | Zbl:1417.37190
- An elementary proof of a theorem by Matsumoto, Nagoya Mathematical Journal, Volume 227 (2017), pp. 77-85 | DOI:10.1017/nmj.2016.48 | Zbl:1408.37073
- On non-contractible periodic orbits for surface homeomorphisms, Ergodic Theory and Dynamical Systems, Volume 36 (2016) no. 5, pp. 1644-1655 | DOI:10.1017/etds.2014.131 | Zbl:1367.37045
- Existence of periodic points near an isolated fixed point with Lefschetz index one and zero rotation for area preserving surface homeomorphisms, Ergodic Theory and Dynamical Systems, Volume 36 (2016) no. 7, pp. 2293-2333 | DOI:10.1017/etds.2015.18 | Zbl:1362.37056
- Towards a dynamical interpretation of Hamiltonian spectral invariants on surfaces, Geometry Topology, Volume 20 (2016) no. 4, p. 2253 | DOI:10.2140/gt.2016.20.2253
- On torus homeomorphisms semiconjugate to irrational rotations, Ergodic Theory and Dynamical Systems, Volume 35 (2015) no. 7, pp. 2114-2137 | DOI:10.1017/etds.2014.23 | Zbl:1352.37125
- Existence of a topological foliation transverse to the dynamics of a homeomorphism, Annales de l'Institut Fourier, Volume 64 (2014) no. 4, pp. 1441-1476 | DOI:10.5802/aif.2886 | Zbl:1352.37126
- Strictly toral dynamics, Inventiones Mathematicae, Volume 196 (2014) no. 2, pp. 339-381 | DOI:10.1007/s00222-013-0470-3 | Zbl:1342.37046
- Bounded and unbounded behavior for area-preserving rational pseudo-rotations, Proceedings of the London Mathematical Society. Third Series, Volume 109 (2014) no. 3, pp. 785-822 | DOI:10.1112/plms/pdu023 | Zbl:1352.37127
- A generalization of the line translation theorem, Transactions of the American Mathematical Society, Volume 366 (2014) no. 11, pp. 5903-5923 | DOI:10.1090/s0002-9947-2014-06096-0 | Zbl:1305.37022
- Some common fixed points for commuting conservative diffeomorphisms of the two-sphere, Journal of the Institute of Mathematics of Jussieu, Volume 12 (2013) no. 4, pp. 821-851 | DOI:10.1017/s1474748012000898 | Zbl:1314.37030
- Existence of orbits with non-zero torsion for certain types of surface diffeomorphisms, Journal of the Mathematical Society of Japan, Volume 65 (2013) no. 1, pp. 137-168 | DOI:10.2969/jmsj/06510137 | Zbl:1268.37064
- On torus homeomorphisms whose rotation set is an interval, Mathematische Zeitschrift, Volume 275 (2013) no. 3-4, pp. 1005-1045 | DOI:10.1007/s00209-013-1168-3 | Zbl:1294.37016
- Prime end rotation numbers of invariant separating continua of annular homeomorphisms, Proceedings of the American Mathematical Society, Volume 140 (2012) no. 3, pp. 839-845 | DOI:10.1090/s0002-9939-2011-11435-7 | Zbl:1255.37018
- Free curves and periodic points for torus homeomorphisms, Ergodic Theory and Dynamical Systems, Volume 28 (2008) no. 6, pp. 1895-1915 | DOI:10.1017/s0143385707001083 | Zbl:1213.37070
- Free lines for homeomorphisms of the open annulus, Transactions of the American Mathematical Society, Volume 360 (2008) no. 4, pp. 2191-2204 | DOI:10.1090/s0002-9947-07-04374-7 | Zbl:1135.37016
- Periodic orbits of Hamiltonian homeomorphisms of surfaces, Duke Mathematical Journal, Volume 133 (2006) no. 1, pp. 125-184 | DOI:10.1215/s0012-7094-06-13315-x | Zbl:1101.37031
- A new proof of Handel's fixed-point theorem, Geometry Topology, Volume 10 (2006), pp. 2299-2349 | DOI:10.2140/gt.2006.10.2299 | Zbl:1126.37027
Cité par 47 documents. Sources : Crossref, zbMATH