We establish a relationship between the helicity of a magnetic flow on a closed surface of genus ≥ 2 and the Mañé critical value.
Paternain, Gabriel P  1
@article{10_2140_agt_2009_9_1413,
author = {Paternain, Gabriel P},
title = {Helicity and the {Ma\~n\'e} critical value},
journal = {Algebraic and Geometric Topology},
pages = {1413--1422},
year = {2009},
volume = {9},
number = {3},
doi = {10.2140/agt.2009.9.1413},
url = {http://geodesic.mathdoc.fr/articles/10.2140/agt.2009.9.1413/}
}
Paternain, Gabriel P. Helicity and the Mañé critical value. Algebraic and Geometric Topology, Tome 9 (2009) no. 3, pp. 1413-1422. doi: 10.2140/agt.2009.9.1413
[1] , On some problems in symplectic topology, from: "Topology and geometry—Rohlin Seminar" (editor O Y Viro), Lecture Notes in Math. 1346, Springer (1988) 1
[2] , , Topological methods in hydrodynamics, Applied Math. Sciences 125, Springer (1998)
[3] , , Anosov magnetic flows, critical values and topological entropy, Nonlinearity 15 (2002) 281
[4] , Eigenvalues in Riemannian geometry, Pure and Applied Math. 115, Academic Press (1984)
[5] , , , Symplectic topology of Mañé's critical values
[6] , , , Periodic orbits for exact magnetic flows on surfaces, Int. Math. Res. Not. (2004) 361
[7] , The unique ergodicity of the horocycle flow, from: "Recent advances in topological dynamics (Proc. Conf., Yale Univ., New Haven, Conn., 1972; in honor of Gustav Arnold Hedlund)" (editor A Beck), Lecture Notes in Math. 318, Springer (1973) 95
[8] , On closed trajectories of a charge in a magnetic field. An application of symplectic geometry, from: "Contact and symplectic geometry (Cambridge, 1994)" (editor C B Thomas), Publ. Newton Inst. 8, Cambridge Univ. Press (1996) 131
[9] , Comments to some of Arnold's problems (1981-9 and related problems and 1994-13), from: "Arnold's problems", Springer-Verlag (2004) 395, 557
[10] , Four applications of conformal equivalence to geometry and dynamics, Ergodic Theory Dynam. Systems 8* (1988) 139
[11] , Lagrangian flows: the dynamics of globally minimizing orbits, Bol. Soc. Brasil. Mat. $($N.S.$)$ 28 (1997) 141
[12] , The degree of knottedness of tangled vortex lines, J. Fluid Mech. 106 (1969) 117
[13] , The Hamiltonian formalism and a multivalued analogue of Morse theory, Uspekhi Mat. Nauk 37 (1982) 3, 248
[14] , Magnetic rigidity of horocycle flows, Pacific J. Math. 225 (2006) 301
[15] , Harmonic analysis and discontinuous groups in weakly symmetric Riemannian spaces with applications to Dirichlet series, J. Indian Math. Soc. $($N.S.$)$ 20 (1956) 47
[16] , The Seiberg–Witten equations and the Weinstein conjecture, Geom. Topol. 11 (2007) 2117
[17] , , The Jones–Witten invariant for flows on a $3$–dimensional manifold, Comm. Math. Phys. 163 (1994) 73
Cité par Sources :