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Time-changes of horocycle flows
Spectral analysis of time changes of horocycle flows
1. | Facultad de Matemáticas, Pontificia Universidad Católica de Chile, Av. Vicuña Mackenna 4860, Santiago, Chile |
References:
[1] |
R. Abraham and J. E. Marsden, "Foundations of Mechanics," Second edition, revised and enlarged, With the assistance of TudorRaţiu and Richard Cushman, Benjamin/Cummings Publishing Co., Inc., Advanced Book Program, Reading, Mass., 1978. |
[2] |
W. O. Amrein, Hilbert space methods in quantum mechanics. Fundamental Sciences, EPFL Press, Lausanne, distributed by CRC Press, Boca Raton, FL, 2009. |
[3] |
W. O. Amrein, A. Boutet de Monveland and V. Georgescu, "$ C_0 $-Groups, Commutator Methods and Spectral Theory of $N$-Body Hamiltonians," Progress in Math., 135, Birkhäuser Verlag, Basel, 1996. |
[4] |
A. Avila, G. Forni and C. Ulcigrai, Mixing for time-changes of heisenberg nilflows, J. Differential Geom., 89 (2011), 369-410. |
[5] |
H. Baumgärtel and M. Wollenberg, Mathematical scattering theory, Mathematische Lehrbücher und Monographien, II. Abteilung: Mathematische Monographien [Mathematical Textbooks and Monographs, Part II: Mathematical Monographs], 59, Akademie-Verlag, Berlin, 1983. |
[6] |
M. B. Bekka and M. Mayer, Ergodic theory and topological dynamics of group actions on homogeneous spaces, London Mathematical Society Lecture Note Series, 269, Cambridge University Press, Cambridge, 2000. |
[7] |
A. Boutet de Monvel and V. Georgescu, The method of differential inequalities, in "Recent Developments in Quantum Mechanics" (Poiana Braşov, 1989), Math. Phys. Stud., 12, Kluwer Acad. Publ., Dordrecht, (1991), 279-298. |
[8] |
I. P. Cornfeld, S. V. Fomin and Y. G. Sinaĭ, "Ergodic Theory," Translated from the Russian by A. B. Sosinskiĭ, Grundlehren derMathematischen Wissenschaften [Fundamental Principles of MathematicalSciences], 245, Springer-Verlag, New York, 1982. |
[9] |
B. Fayad, Partially mixing and locally rank 1 smooth transformations and flows on the torus Td,$d $≥$ 3$, J. London Math. Soc. (2), 64 (2001), 637-654. |
[10] |
B. Fayad, Smooth mixing flows with purely singular spectra, Duke Math. J., 132 (2006), 371-391.
doi: 10.1215/S0012-7094-06-13225-8. |
[11] |
B. Fayad, A. Katok and A. Windsor, Mixed spectrum reparameterizations of linear flows on $\mathbb T^2$, Dedicated to the memory of I. G. Petrovskii on the occasion of his 100th anniversary, Mosc. Math. J., 1 (2001), 521-537, 644. |
[12] |
C. Fernández, S. Richard and R. Tiedra de Aldecoa, Commutator methods for unitary operators, J. Spectr. Theory, to appear, arXiv:1112.0167. |
[13] |
G. Forni and C. Ulcigrai, Time-changes of horocycle flows, preprint, arXiv:1202.4986. |
[14] |
K. Gelfert and A. E. Motter, (Non)invariance of dynamical quantities for orbit equivalent flows, Comm. Math. Phys., 300 (2010), 411-433.
doi: 10.1007/s00220-010-1120-x. |
[15] |
G. A. Hedlund, Fuchsian groups and mixtures, Ann. of Math. (2), 40 (1939), 370-383. |
[16] |
P. D. Humphries, Change of velocity in dynamical systems, J. London Math. Soc. (2), 7 (1974), 747-757.
doi: 10.1112/jlms/s2-7.4.747. |
[17] |
A. Katok and J.-P. Thouvenot, Spectral properties and combinatorial constructions in ergodic theory, in "Handbook of Dynamical Systems," Vol. 1B, Elsevier B. V., Amsterdam, (2006), 649-743.
doi: 10.1016/S1874-575X(06)80036-6. |
[18] |
A. G. Kushnirenko, Spectral properties of certain dynamical systems with polynomial dispersal, Moscow Univ. Math. Bull., 29 (1974), 82-87. |
[19] |
B. Marcus, The horocycle flow is mixing of all degrees, Invent. Math., 46 (1978), 201-209.
doi: 10.1007/BF01390274. |
[20] |
É. Mourre, Absence of singular continuous spectrum for certain selfadjoint operators, Comm. Math. Phys., 78 (1980/81), 391-408.
doi: 10.1007/BF01942331. |
[21] |
O. S. Parasyuk, Flows of horocycles on surfaces of constant negative curvature, Uspehi Matem. Nauk (N.S.), 8 (1953), 125-126. |
[22] |
W. Parry, "Topics in Ergodic Theory," Cambridge Tracts in Mathematics, 75, Cambridge University Press, Cambridge-New York, 1981. |
[23] |
J. Sahbani, The conjugate operator method for locally regular Hamiltonians, J. Operator Theory, 38 (1997), 297-322. |
[24] |
H. Totoki, Time changes of flows, Mem. Fac. Sci. Kyushu Univ. Ser. A, 20 (1966), 27-55.
doi: 10.2206/kyushumfs.20.27. |
show all references
References:
[1] |
R. Abraham and J. E. Marsden, "Foundations of Mechanics," Second edition, revised and enlarged, With the assistance of TudorRaţiu and Richard Cushman, Benjamin/Cummings Publishing Co., Inc., Advanced Book Program, Reading, Mass., 1978. |
[2] |
W. O. Amrein, Hilbert space methods in quantum mechanics. Fundamental Sciences, EPFL Press, Lausanne, distributed by CRC Press, Boca Raton, FL, 2009. |
[3] |
W. O. Amrein, A. Boutet de Monveland and V. Georgescu, "$ C_0 $-Groups, Commutator Methods and Spectral Theory of $N$-Body Hamiltonians," Progress in Math., 135, Birkhäuser Verlag, Basel, 1996. |
[4] |
A. Avila, G. Forni and C. Ulcigrai, Mixing for time-changes of heisenberg nilflows, J. Differential Geom., 89 (2011), 369-410. |
[5] |
H. Baumgärtel and M. Wollenberg, Mathematical scattering theory, Mathematische Lehrbücher und Monographien, II. Abteilung: Mathematische Monographien [Mathematical Textbooks and Monographs, Part II: Mathematical Monographs], 59, Akademie-Verlag, Berlin, 1983. |
[6] |
M. B. Bekka and M. Mayer, Ergodic theory and topological dynamics of group actions on homogeneous spaces, London Mathematical Society Lecture Note Series, 269, Cambridge University Press, Cambridge, 2000. |
[7] |
A. Boutet de Monvel and V. Georgescu, The method of differential inequalities, in "Recent Developments in Quantum Mechanics" (Poiana Braşov, 1989), Math. Phys. Stud., 12, Kluwer Acad. Publ., Dordrecht, (1991), 279-298. |
[8] |
I. P. Cornfeld, S. V. Fomin and Y. G. Sinaĭ, "Ergodic Theory," Translated from the Russian by A. B. Sosinskiĭ, Grundlehren derMathematischen Wissenschaften [Fundamental Principles of MathematicalSciences], 245, Springer-Verlag, New York, 1982. |
[9] |
B. Fayad, Partially mixing and locally rank 1 smooth transformations and flows on the torus Td,$d $≥$ 3$, J. London Math. Soc. (2), 64 (2001), 637-654. |
[10] |
B. Fayad, Smooth mixing flows with purely singular spectra, Duke Math. J., 132 (2006), 371-391.
doi: 10.1215/S0012-7094-06-13225-8. |
[11] |
B. Fayad, A. Katok and A. Windsor, Mixed spectrum reparameterizations of linear flows on $\mathbb T^2$, Dedicated to the memory of I. G. Petrovskii on the occasion of his 100th anniversary, Mosc. Math. J., 1 (2001), 521-537, 644. |
[12] |
C. Fernández, S. Richard and R. Tiedra de Aldecoa, Commutator methods for unitary operators, J. Spectr. Theory, to appear, arXiv:1112.0167. |
[13] |
G. Forni and C. Ulcigrai, Time-changes of horocycle flows, preprint, arXiv:1202.4986. |
[14] |
K. Gelfert and A. E. Motter, (Non)invariance of dynamical quantities for orbit equivalent flows, Comm. Math. Phys., 300 (2010), 411-433.
doi: 10.1007/s00220-010-1120-x. |
[15] |
G. A. Hedlund, Fuchsian groups and mixtures, Ann. of Math. (2), 40 (1939), 370-383. |
[16] |
P. D. Humphries, Change of velocity in dynamical systems, J. London Math. Soc. (2), 7 (1974), 747-757.
doi: 10.1112/jlms/s2-7.4.747. |
[17] |
A. Katok and J.-P. Thouvenot, Spectral properties and combinatorial constructions in ergodic theory, in "Handbook of Dynamical Systems," Vol. 1B, Elsevier B. V., Amsterdam, (2006), 649-743.
doi: 10.1016/S1874-575X(06)80036-6. |
[18] |
A. G. Kushnirenko, Spectral properties of certain dynamical systems with polynomial dispersal, Moscow Univ. Math. Bull., 29 (1974), 82-87. |
[19] |
B. Marcus, The horocycle flow is mixing of all degrees, Invent. Math., 46 (1978), 201-209.
doi: 10.1007/BF01390274. |
[20] |
É. Mourre, Absence of singular continuous spectrum for certain selfadjoint operators, Comm. Math. Phys., 78 (1980/81), 391-408.
doi: 10.1007/BF01942331. |
[21] |
O. S. Parasyuk, Flows of horocycles on surfaces of constant negative curvature, Uspehi Matem. Nauk (N.S.), 8 (1953), 125-126. |
[22] |
W. Parry, "Topics in Ergodic Theory," Cambridge Tracts in Mathematics, 75, Cambridge University Press, Cambridge-New York, 1981. |
[23] |
J. Sahbani, The conjugate operator method for locally regular Hamiltonians, J. Operator Theory, 38 (1997), 297-322. |
[24] |
H. Totoki, Time changes of flows, Mem. Fac. Sci. Kyushu Univ. Ser. A, 20 (1966), 27-55.
doi: 10.2206/kyushumfs.20.27. |
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