-
Previous Article
New infinite families of pseudo-Anosov maps with vanishing Sah-Arnoux-Fathi invariant
- JMD Home
- This Volume
-
Next Article
Positive topological entropy for Reeb flows on 3-dimensional Anosov contact manifolds
Mean action and the Calabi invariant
1. | Department of Mathematics, 970 Evans Hall, University of California, Berkeley, CA 94720, United States |
References:
[1] |
A. Abbondandolo, B. Bramham, U. Hryniewicz and P. Salamão, Sharp systolic inequalities for Reeb flows on the three-sphere,, , ().
|
[2] |
E. Calabi, On the group of automorphisms of a symplectic manifold, in Problems in Analysis (Lectures at the Sympos. in honor of S. Bochner, Princeton Univ., Princeton, N.J., 1969) (ed. R. C. Gunning), Princeton Univ. Press, Princeton, 1970, 1-26. |
[3] |
V. Colin, P. Ghiggini and K. Honda, Embedded contact homology and open book decompositions,, , ().
|
[4] |
D. Cristofaro-Gardiner, The absolute gradings on embedded contact homology and Seiberg-Witten Floer cohomology, Algebr. Geom. Topol., 13 (2013), 2239-2260.
doi: 10.2140/agt.2013.13.2239. |
[5] |
D. Cristofaro-Gardiner, M. Hutchings and V. Ramos, The asymptotics of ECH capacities, Invent. Math., 199 (2015), 187-214.
doi: 10.1007/s00222-014-0510-7. |
[6] |
Y. Eliashberg, Legendrian and transversal knots in tight contact 3-manifolds, in Topological Methods in Modern Mathematics, Publish or Perish, Houston, TX, 1993, 171-193. |
[7] |
M. Entov and L. Polterovich, Calabi quasimorphism and quantum homology, Int. Math. Res. Not., (2003), 1635-1676.
doi: 10.1155/S1073792803210011. |
[8] |
J. Etnyre, Legendrian and transversal knots, in Handbook of Knot Theory, Elsevier B. V., Amsterdam, 2005, 105-185.
doi: 10.1016/B978-044451452-3/50004-6. |
[9] |
J. Franks, Area preserving homeomorphisms of open surfaces of genus zero, New York J. Math., 2 (1996), 1-19. |
[10] |
J.-M. Gambaudo and É. Ghys, Enlacements asymptotiques, Topology, 36 (1997), 1355-1379.
doi: 10.1016/S0040-9383(97)00001-3. |
[11] |
H. Hofer, K. Wysocki and E. Zehnder, Properties of pseudo-holomorphic curves in symplectizations. II. Embedding controls and algebraic invariants, Geom. and Func. Anal., 5 (1995), 270-328.
doi: 10.1007/BF01895669. |
[12] |
H. Hofer, K. Wysocki and E. Zehnder, The dynamics on three-dimensional strictly convex energy surfaces, Ann. of Math. (2), 148 (1998), 197-289.
doi: 10.2307/120994. |
[13] |
H. Hofer, K. Wysock and E. Zehnder, Finite energy foliations of tight three-spheres and Hamiltonian dynamics, Ann. of Math. (2), 157 (2003), 125-255.
doi: 10.4007/annals.2003.157.125. |
[14] |
M. Hutchings, Quantitative embedded contact homology, J. Diff. Geom., 88 (2011), 231-266. |
[15] |
M. Hutchings, Lecture notes on embedded contact homology, in Contact and Symplectic Topology, Bolyai Soc. Math. Stud., 26, János Bolyai Math. Soc., Budapest, 2014, 389-484.
doi: 10.1007/978-3-319-02036-5_9. |
[16] |
M. Hutchings, Embedded contact homology as a (symplectic) field theory,, in preparation., ().
|
[17] |
M. Hutchings and C. H. Taubes, Gluing pseudoholomorphic curves along branched covered cylinders I, J. Symplectic Geom., 5 (2007), 43-137.
doi: 10.4310/JSG.2007.v5.n1.a5. |
[18] |
M. Hutchings and C. H. Taubes, Gluing pseudoholomorphic curves along branched covered cylinders II, J. Symplectic Geom., 7 (2009), 29-133.
doi: 10.4310/JSG.2009.v7.n1.a2. |
[19] |
M. Hutchings and C. H. Taubes, Proof of the Arnold chord conjecture in three dimensions, II, Geom. Topol., 17 (2013), 2601-2688.
doi: 10.2140/gt.2013.17.2601. |
[20] |
P. B. Kronheimer and T. S. Mrowka, Monopoles and Three-Manifolds, Cambridge Univ. Press, 2007.
doi: 10.1017/CBO9780511543111. |
[21] |
R. Siefring, Relative asymptotic behavior of pseudoholomorphic half-cylinders, Comm. Pure Appl. Math., 61 (2008), 1631-1684.
doi: 10.1002/cpa.20224. |
[22] |
C. H. Taubes, Embedded contact homology and Seiberg-Witten Floer homology I, Geom. Topol., 14 (2010), 2497-2581.
doi: 10.2140/gt.2010.14.2497. |
show all references
References:
[1] |
A. Abbondandolo, B. Bramham, U. Hryniewicz and P. Salamão, Sharp systolic inequalities for Reeb flows on the three-sphere,, , ().
|
[2] |
E. Calabi, On the group of automorphisms of a symplectic manifold, in Problems in Analysis (Lectures at the Sympos. in honor of S. Bochner, Princeton Univ., Princeton, N.J., 1969) (ed. R. C. Gunning), Princeton Univ. Press, Princeton, 1970, 1-26. |
[3] |
V. Colin, P. Ghiggini and K. Honda, Embedded contact homology and open book decompositions,, , ().
|
[4] |
D. Cristofaro-Gardiner, The absolute gradings on embedded contact homology and Seiberg-Witten Floer cohomology, Algebr. Geom. Topol., 13 (2013), 2239-2260.
doi: 10.2140/agt.2013.13.2239. |
[5] |
D. Cristofaro-Gardiner, M. Hutchings and V. Ramos, The asymptotics of ECH capacities, Invent. Math., 199 (2015), 187-214.
doi: 10.1007/s00222-014-0510-7. |
[6] |
Y. Eliashberg, Legendrian and transversal knots in tight contact 3-manifolds, in Topological Methods in Modern Mathematics, Publish or Perish, Houston, TX, 1993, 171-193. |
[7] |
M. Entov and L. Polterovich, Calabi quasimorphism and quantum homology, Int. Math. Res. Not., (2003), 1635-1676.
doi: 10.1155/S1073792803210011. |
[8] |
J. Etnyre, Legendrian and transversal knots, in Handbook of Knot Theory, Elsevier B. V., Amsterdam, 2005, 105-185.
doi: 10.1016/B978-044451452-3/50004-6. |
[9] |
J. Franks, Area preserving homeomorphisms of open surfaces of genus zero, New York J. Math., 2 (1996), 1-19. |
[10] |
J.-M. Gambaudo and É. Ghys, Enlacements asymptotiques, Topology, 36 (1997), 1355-1379.
doi: 10.1016/S0040-9383(97)00001-3. |
[11] |
H. Hofer, K. Wysocki and E. Zehnder, Properties of pseudo-holomorphic curves in symplectizations. II. Embedding controls and algebraic invariants, Geom. and Func. Anal., 5 (1995), 270-328.
doi: 10.1007/BF01895669. |
[12] |
H. Hofer, K. Wysocki and E. Zehnder, The dynamics on three-dimensional strictly convex energy surfaces, Ann. of Math. (2), 148 (1998), 197-289.
doi: 10.2307/120994. |
[13] |
H. Hofer, K. Wysock and E. Zehnder, Finite energy foliations of tight three-spheres and Hamiltonian dynamics, Ann. of Math. (2), 157 (2003), 125-255.
doi: 10.4007/annals.2003.157.125. |
[14] |
M. Hutchings, Quantitative embedded contact homology, J. Diff. Geom., 88 (2011), 231-266. |
[15] |
M. Hutchings, Lecture notes on embedded contact homology, in Contact and Symplectic Topology, Bolyai Soc. Math. Stud., 26, János Bolyai Math. Soc., Budapest, 2014, 389-484.
doi: 10.1007/978-3-319-02036-5_9. |
[16] |
M. Hutchings, Embedded contact homology as a (symplectic) field theory,, in preparation., ().
|
[17] |
M. Hutchings and C. H. Taubes, Gluing pseudoholomorphic curves along branched covered cylinders I, J. Symplectic Geom., 5 (2007), 43-137.
doi: 10.4310/JSG.2007.v5.n1.a5. |
[18] |
M. Hutchings and C. H. Taubes, Gluing pseudoholomorphic curves along branched covered cylinders II, J. Symplectic Geom., 7 (2009), 29-133.
doi: 10.4310/JSG.2009.v7.n1.a2. |
[19] |
M. Hutchings and C. H. Taubes, Proof of the Arnold chord conjecture in three dimensions, II, Geom. Topol., 17 (2013), 2601-2688.
doi: 10.2140/gt.2013.17.2601. |
[20] |
P. B. Kronheimer and T. S. Mrowka, Monopoles and Three-Manifolds, Cambridge Univ. Press, 2007.
doi: 10.1017/CBO9780511543111. |
[21] |
R. Siefring, Relative asymptotic behavior of pseudoholomorphic half-cylinders, Comm. Pure Appl. Math., 61 (2008), 1631-1684.
doi: 10.1002/cpa.20224. |
[22] |
C. H. Taubes, Embedded contact homology and Seiberg-Witten Floer homology I, Geom. Topol., 14 (2010), 2497-2581.
doi: 10.2140/gt.2010.14.2497. |
[1] |
Al Momin. Contact homology of orbit complements and implied existence. Journal of Modern Dynamics, 2011, 5 (3) : 409-472. doi: 10.3934/jmd.2011.5.409 |
[2] |
Asaf Kislev. Compactly supported Hamiltonian loops with a non-zero Calabi invariant. Electronic Research Announcements, 2014, 21: 80-88. doi: 10.3934/era.2014.21.80 |
[3] |
Qihuai Liu, Pedro J. Torres. Orbital dynamics on invariant sets of contact Hamiltonian systems. Discrete and Continuous Dynamical Systems - B, 2021 doi: 10.3934/dcdsb.2021297 |
[4] |
Radu Saghin. Note on homology of expanding foliations. Discrete and Continuous Dynamical Systems - S, 2009, 2 (2) : 349-360. doi: 10.3934/dcdss.2009.2.349 |
[5] |
Hongnian Huang. On the extension and smoothing of the Calabi flow on complex tori. Discrete and Continuous Dynamical Systems, 2017, 37 (12) : 6153-6164. doi: 10.3934/dcds.2017265 |
[6] |
Gianne Derks, Sara Maad, Björn Sandstede. Perturbations of embedded eigenvalues for the bilaplacian on a cylinder. Discrete and Continuous Dynamical Systems, 2008, 21 (3) : 801-821. doi: 10.3934/dcds.2008.21.801 |
[7] |
Octav Cornea and Francois Lalonde. Cluster homology: An overview of the construction and results. Electronic Research Announcements, 2006, 12: 1-12. |
[8] |
Stephen Coughlan, Łukasz Gołębiowski, Grzegorz Kapustka, Michał Kapustka. Arithmetically Gorenstein Calabi--Yau threefolds in $\mathbb{P}^7$. Electronic Research Announcements, 2016, 23: 52-68. doi: 10.3934/era.2016.23.006 |
[9] |
S. Aiello, Luigi Barletti, Aldo Belleni-Morante. Identification of photon sources, stochastically embedded in an interstellar cloud. Kinetic and Related Models, 2009, 2 (3) : 425-432. doi: 10.3934/krm.2009.2.425 |
[10] |
Ephraim Agyingi, Tamas Wiandt, Sophia A. Maggelakis. Thermal detection of a prevascular tumor embedded in breast tissue. Mathematical Biosciences & Engineering, 2015, 12 (5) : 907-915. doi: 10.3934/mbe.2015.12.907 |
[11] |
John Guckenheimer. Continuation methods for principal foliations of embedded surfaces. Journal of Computational Dynamics, 2022 doi: 10.3934/jcd.2022007 |
[12] |
Sonja Hohloch. Transport, flux and growth of homoclinic Floer homology. Discrete and Continuous Dynamical Systems, 2012, 32 (10) : 3587-3620. doi: 10.3934/dcds.2012.32.3587 |
[13] |
Sarah Day; William D. Kalies; Konstantin Mischaikow and Thomas Wanner. Probabilistic and numerical validation of homology computations for nodal domains. Electronic Research Announcements, 2007, 13: 60-73. |
[14] |
Mark Pollicott. Closed orbits and homology for $C^2$-flows. Discrete and Continuous Dynamical Systems, 1999, 5 (3) : 529-534. doi: 10.3934/dcds.1999.5.529 |
[15] |
Fabian Ziltener. Note on coisotropic Floer homology and leafwise fixed points. Electronic Research Archive, 2021, 29 (4) : 2553-2560. doi: 10.3934/era.2021001 |
[16] |
Alexander Fauck, Will J. Merry, Jagna Wiśniewska. Computing the Rabinowitz Floer homology of tentacular hyperboloids. Journal of Modern Dynamics, 2021, 17: 353-399. doi: 10.3934/jmd.2021013 |
[17] |
Xinlin Cao, Yi-Hsuan Lin, Hongyu Liu. Simultaneously recovering potentials and embedded obstacles for anisotropic fractional Schrödinger operators. Inverse Problems and Imaging, 2019, 13 (1) : 197-210. doi: 10.3934/ipi.2019011 |
[18] |
Anthony M. Bloch, Peter E. Crouch, Nikolaj Nordkvist, Amit K. Sanyal. Embedded geodesic problems and optimal control for matrix Lie groups. Journal of Geometric Mechanics, 2011, 3 (2) : 197-223. doi: 10.3934/jgm.2011.3.197 |
[19] |
Yossi Bokor, Katharine Turner, Christopher Williams. Reconstructing linearly embedded graphs: A first step to stratified space learning. Foundations of Data Science, 2021 doi: 10.3934/fods.2021026 |
[20] |
Xin Xu, Jessi Cisewski-Kehe. EmT: Locating empty territories of homology group generators in a dataset. Foundations of Data Science, 2019, 1 (2) : 227-247. doi: 10.3934/fods.2019010 |
2020 Impact Factor: 0.848
Tools
Metrics
Other articles
by authors
[Back to Top]