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Équidistribution, comptage et approximation par irrationnels quadratiques
On primes and period growth for Hamiltonian diffeomorphisms
1. | Department of Mathematics, University of Illinois at Urbana-Champaign, Urbana, IL 61801 |
References:
[1] |
V. I. Arnol'd, "Mathematical Methods of Classical Mechanics,", Second edition, 60 (1989).
|
[2] |
B. Collier, E. Kerman, B. Reiniger, B. Turmunkh and A. Zimmer, A symplectic proof of a theorem of Franks,, preprint, (). Google Scholar |
[3] |
C. Conley and E. Zehnder, Morse-type index theory for flows and periodic solutions for Hamiltonian equations,, Comm. Pure Appl. Math., 37 (1984), 207.
doi: 10.1002/cpa.3160370204. |
[4] |
A. Cotton-Clay, Symplectic Floer homology of area-preserving surface diffeomorphisms,, Geom. Topol., 13 (2009), 2619.
doi: 10.2140/gt.2009.13.2619. |
[5] |
A. Cotton-Clay, A sharp bound on fixed points of area-preserving surface diffeomorphisms,, preprint, (). Google Scholar |
[6] |
S. Dostoglou and D. A. Salamon, Self-dual instantons and holomorphic curves,, Ann. of Math. (2), 139 (1994), 581.
|
[7] |
A. Floer, Morse theory for Lagrangian intersections,, J. Diff. Geom., 28 (1988), 513.
|
[8] |
J. Franks, Geodesics on $S^2$ and periodic points of annulus homeomorphisms,, Invent. Math., 108 (1992), 403.
doi: 10.1007/BF02100612. |
[9] |
J. Franks, Area preserving homeomorphisms of open surfaces of genus zero,, New York Jour. of Math., 2 (1996), 1.
|
[10] |
J. Franks and M. Handel, Periodic points of Hamiltonian surface diffeomorphisms,, Geom. Topol., 7 (2003), 713.
doi: 10.2140/gt.2003.7.713. |
[11] |
V. L. Ginzburg, The Conley conjecture,, Ann. of Math. (2), 172 (2010), 1127.
doi: 10.4007/annals.2010.172.1129. |
[12] |
V. L. Ginzburg and B. Z. Gürel, Action and index spectra and periodic orbits in Hamiltonian dynamics,, Geom. Topol., 13 (2009), 2745.
doi: 10.2140/gt.2009.13.2745. |
[13] |
V. L. Ginzburg and E. Kerman, Homological resonances for Hamiltonian diffeomorphisms and Reeb flows,, Internat. Math. Res. Notices, 2010 (): 53.
doi: 10.1093/imrn/rnp120. |
[14] |
G. Harman, Simultaneous Diophantine approximation with primes,, J. London Math. Soc. (2), 39 (1989), 405.
doi: 10.1112/jlms/s2-39.3.405. |
[15] |
N. Hingston, Subharmonic solutions of Hamiltonian equations on tori,, Ann. of Math. (2), 170 (2009), 529.
doi: 10.4007/annals.2009.170.529. |
[16] |
H. V. Lê and K. Ono, Symplectic fixed points, the Calabi invariant and Novikov homology,, Topology, 34 (1995), 155.
doi: 10.1016/0040-9383(94)E0015-C. |
[17] |
Y. Long, "Index Theory for Symplectic Paths with Applications,", Progr. Math., 207 (2002).
|
[18] |
D. Salamon and E. Zehnder, Morse theory for periodic solutions of Hamiltonian systems and the Maslov index,, Comm. Pure Appl. Math., 45 (1992), 1303.
doi: 10.1002/cpa.3160451004. |
[19] |
P. Seidel, "Floer Homology and the Symplectic Isotopy Problem,", D. Phil thesis, (1997). Google Scholar |
[20] |
P. Seidel, $\pi_1$ of symplectic automorphism groups and invertibles in quantum homology rings,, Geom. Funct. Anal., 7 (1997), 1046.
doi: 10.1007/s000390050037. |
[21] |
P. Seidel, Symplectic Floer homology and the mapping class group,, Pac. J. Math., 206 (2002), 219.
doi: 10.2140/pjm.2002.206.219. |
[22] |
P. Seidel, Braids and symplectic four-manifolds with abelian fundamental group,, Turkish J. Math., 26 (2002), 93.
|
[23] |
I. M. Vinogradov, "The Method of Trigonometric Sums in the Theory of Numbers,", Translated from the Russian, (1954).
|
show all references
References:
[1] |
V. I. Arnol'd, "Mathematical Methods of Classical Mechanics,", Second edition, 60 (1989).
|
[2] |
B. Collier, E. Kerman, B. Reiniger, B. Turmunkh and A. Zimmer, A symplectic proof of a theorem of Franks,, preprint, (). Google Scholar |
[3] |
C. Conley and E. Zehnder, Morse-type index theory for flows and periodic solutions for Hamiltonian equations,, Comm. Pure Appl. Math., 37 (1984), 207.
doi: 10.1002/cpa.3160370204. |
[4] |
A. Cotton-Clay, Symplectic Floer homology of area-preserving surface diffeomorphisms,, Geom. Topol., 13 (2009), 2619.
doi: 10.2140/gt.2009.13.2619. |
[5] |
A. Cotton-Clay, A sharp bound on fixed points of area-preserving surface diffeomorphisms,, preprint, (). Google Scholar |
[6] |
S. Dostoglou and D. A. Salamon, Self-dual instantons and holomorphic curves,, Ann. of Math. (2), 139 (1994), 581.
|
[7] |
A. Floer, Morse theory for Lagrangian intersections,, J. Diff. Geom., 28 (1988), 513.
|
[8] |
J. Franks, Geodesics on $S^2$ and periodic points of annulus homeomorphisms,, Invent. Math., 108 (1992), 403.
doi: 10.1007/BF02100612. |
[9] |
J. Franks, Area preserving homeomorphisms of open surfaces of genus zero,, New York Jour. of Math., 2 (1996), 1.
|
[10] |
J. Franks and M. Handel, Periodic points of Hamiltonian surface diffeomorphisms,, Geom. Topol., 7 (2003), 713.
doi: 10.2140/gt.2003.7.713. |
[11] |
V. L. Ginzburg, The Conley conjecture,, Ann. of Math. (2), 172 (2010), 1127.
doi: 10.4007/annals.2010.172.1129. |
[12] |
V. L. Ginzburg and B. Z. Gürel, Action and index spectra and periodic orbits in Hamiltonian dynamics,, Geom. Topol., 13 (2009), 2745.
doi: 10.2140/gt.2009.13.2745. |
[13] |
V. L. Ginzburg and E. Kerman, Homological resonances for Hamiltonian diffeomorphisms and Reeb flows,, Internat. Math. Res. Notices, 2010 (): 53.
doi: 10.1093/imrn/rnp120. |
[14] |
G. Harman, Simultaneous Diophantine approximation with primes,, J. London Math. Soc. (2), 39 (1989), 405.
doi: 10.1112/jlms/s2-39.3.405. |
[15] |
N. Hingston, Subharmonic solutions of Hamiltonian equations on tori,, Ann. of Math. (2), 170 (2009), 529.
doi: 10.4007/annals.2009.170.529. |
[16] |
H. V. Lê and K. Ono, Symplectic fixed points, the Calabi invariant and Novikov homology,, Topology, 34 (1995), 155.
doi: 10.1016/0040-9383(94)E0015-C. |
[17] |
Y. Long, "Index Theory for Symplectic Paths with Applications,", Progr. Math., 207 (2002).
|
[18] |
D. Salamon and E. Zehnder, Morse theory for periodic solutions of Hamiltonian systems and the Maslov index,, Comm. Pure Appl. Math., 45 (1992), 1303.
doi: 10.1002/cpa.3160451004. |
[19] |
P. Seidel, "Floer Homology and the Symplectic Isotopy Problem,", D. Phil thesis, (1997). Google Scholar |
[20] |
P. Seidel, $\pi_1$ of symplectic automorphism groups and invertibles in quantum homology rings,, Geom. Funct. Anal., 7 (1997), 1046.
doi: 10.1007/s000390050037. |
[21] |
P. Seidel, Symplectic Floer homology and the mapping class group,, Pac. J. Math., 206 (2002), 219.
doi: 10.2140/pjm.2002.206.219. |
[22] |
P. Seidel, Braids and symplectic four-manifolds with abelian fundamental group,, Turkish J. Math., 26 (2002), 93.
|
[23] |
I. M. Vinogradov, "The Method of Trigonometric Sums in the Theory of Numbers,", Translated from the Russian, (1954).
|
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