Geodesic
Classical and Quantum Dynamics on Orbifolds
Symmetry, integrability and geometry: methods and applications, Tome 7 (2011) Cet article a éte moissonné depuis la source Math-Net.Ru

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We present two versions of the Egorov theorem for orbifolds. The first one is a straightforward extension of the classical theorem for smooth manifolds. The second one considers an orbifold as a singular manifold, the orbit space of a Lie group action, and deals with the corresponding objects in noncommutative geometry.
Keywords: microlocal analysis, noncommutative geometry, symplectic reduction, orbifold, Hamiltonian dynamics, elliptic operators.
Mots-clés : quantization, foliation 
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     author = {Yuri A. Kordyukov},
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Yuri A. Kordyukov. Classical and Quantum Dynamics on Orbifolds. Symmetry, integrability and geometry: methods and applications, Tome 7 (2011). http://geodesic.mathdoc.fr/item/SIGMA_2011_7_a105/

[1] Adem A., Leida J., Ruan Y., Orbifolds and stringy topology, Cambridge Tracts in Mathematics, 171, Cambridge University Press, Cambridge, 2007 | DOI | MR | Zbl

[2] Bucicovschi B., Seeley's theory of pseudodifferential operators on orbifolds, arXiv: math.DG/9912228

[3] Dryden E.B., Gordon C.S., Greenwald S.J., Webb D.L., “Asymptotic expansion of the heat kernel for orbifolds”, Michigan Math. J., 56 (2008), 205–238 | DOI | MR | Zbl

[4] Girbau J., Nicolau M., “Pseudodifferential operators on $V$-manifolds and foliations. I”, Collect. Math., 30 (1979), 247–265 | MR | Zbl

[5] Girbau J., Nicolau M., “Pseudodifferential operators on $V$-manifolds and foliations. II”, Collect. Math., 31 (1980), 63–95 | MR

[6] Guillemin V., Uribe A., Wang Z., “Geodesics on weighted projective spaces”, Ann. Global Anal. Geom., 36 (2009), 205–220 ; arXiv: 0805.1003 | DOI | MR | Zbl

[7] Jakobson D., Strohmaier A., “High energy limits of Laplace-type and Dirac-type eigenfunctions and frame flows”, Comm. Math. Phys., 270 (2007), 813–833 ; arXiv: math.SP/0607616 | DOI | MR | Zbl

[8] Kawasaki T., “The signature theorem for $V$-manifolds”, Topology, 17 (1978), 75–83 | DOI | MR

[9] Kawasaki T., “The index of elliptic operators over $V$-manifolds”, Nagoya Math. J., 84 (1981), 135–157 | MR | Zbl

[10] Kordyukov Yu.A., “Noncommutative spectral geometry of Riemannian foliations”, Manuscripta Math., 94 (1997), 45–73 | DOI | MR | Zbl

[11] Kordyukov Yu.A., “Egorov's theorem for transversally elliptic operators on foliated manifolds and noncommutative geodesic flow”, Math. Phys. Anal. Geom., 8 (2005), 97–119 ; arXiv: math.DG/0407435 | DOI | MR | Zbl

[12] Kordyukov Yu.A., “The Egorov theorem for transverse Dirac-type operators on foliated manifolds”, J. Geom. Phys., 57 (2007), 2345–2364 ; arXiv: 0708.1660 | DOI | MR | Zbl

[13] Kordyukov Yu.A., “Noncommutative Hamiltonian dynamics on foliated manifolds”, J. Fixed Point Theory Appl., 7 (2010), 385–399 ; arXiv: 0912.1923 | DOI | MR | Zbl

[14] Marsden J., Weinstein A., “Reduction of symplectic manifolds with symmetry”, Rep. Math. Phys., 5 (1974), 121–130 | DOI | MR | Zbl

[15] Moerdijk I., Mrčun J., Introduction to foliations and Lie groupoids, Cambridge Studies in Advanced Mathematics, 91, Cambridge University Press, Cambridge, 2003 | DOI | MR | Zbl

[16] Sjamaar R., Lerman E., “Stratified symplectic spaces and reduction”, Ann. of Math. (2), 134 (1991), 375–422 | DOI | MR | Zbl

[17] Stanhope E., Uribe A., “The spectral function of a Riemannian orbifold”, Ann. Global Anal. Geom., 40 (2011), 47–65 | DOI | MR | Zbl