메뉴 건너뛰기




Volumn 31, Issue 2, 2007, Pages 155-180

On geodesic exponential maps of the Virasoro group

Author keywords

Geodesic exponential maps; Virasoro group

Indexed keywords


EID: 33847253064     PISSN: 0232704X     EISSN: None     Source Type: Journal    
DOI: 10.1007/s10455-006-9042-8     Document Type: Article
Times cited : (142)

References (33)
  • 1
    • 0001356905 scopus 로고
    • Sur la geometrié differentielle des groupes de Lie de dimension infinie et ses applications à l'hydrodynamique des fluids parfaits
    • Arnold, V.: Sur la geometrié differentielle des groupes de Lie de dimension infinie et ses applications à l'hydrodynamique des fluids parfaits. Ann. Inst. Fourier 16(1), 319-361 (1966)
    • (1966) Ann. Inst. Fourier , vol.16 , Issue.1 , pp. 319-361
    • Arnold, V.1
  • 4
    • 77956834067 scopus 로고
    • A mathematical model illustrating the theory of turbulence
    • Burgers, J.: A mathematical model illustrating the theory of turbulence. Adv. Appl. Mech. 1, 171-199 (1948)
    • (1948) Adv. Appl. Mech , vol.1 , pp. 171-199
    • Burgers, J.1
  • 5
    • 12044254491 scopus 로고
    • An integrable shallow water equation with peaked solitons
    • Camassa, R., Holm, D.: An integrable shallow water equation with peaked solitons. Phys. Rev. Lett. 71, 1661-1664 (1993)
    • (1993) Phys. Rev. Lett , vol.71 , pp. 1661-1664
    • Camassa, R.1    Holm, D.2
  • 6
    • 0000213450 scopus 로고    scopus 로고
    • On the Cauchy problem for the periodic Camassa-Holm equation
    • Constantin, A.: On the Cauchy problem for the periodic Camassa-Holm equation. J. Differential Equations 141, 218-235 (1997)
    • (1997) J. Differential Equations , vol.141 , pp. 218-235
    • Constantin, A.1
  • 7
    • 0032374820 scopus 로고    scopus 로고
    • Well-posedness, global existence, and blow-up phenomena for a periodic quasi-linear hyperbolic equation
    • Constantin, A., Escher, J.: Well-posedness, global existence, and blow-up phenomena for a periodic quasi-linear hyperbolic equation. Comm. Pure Appl. Math. 51, 475-504 (1998)
    • (1998) Comm. Pure Appl. Math , vol.51 , pp. 475-504
    • Constantin, A.1    Escher, J.2
  • 8
    • 0034347295 scopus 로고    scopus 로고
    • On the blow-up rate and the blow-up set of breaking waves for a shallow water equation
    • Constantin, A., Escher, J.: On the blow-up rate and the blow-up set of breaking waves for a shallow water equation. Math. Z. 233, 75-91 (2000)
    • (2000) Math. Z , vol.233 , pp. 75-91
    • Constantin, A.1    Escher, J.2
  • 9
    • 0033415933 scopus 로고    scopus 로고
    • A shallow water equation on the circle
    • Constantin, A., McKean, H.: A shallow water equation on the circle. Comm. Pure Appl. Math. 52, 949-982 (1999)
    • (1999) Comm. Pure Appl. Math , vol.52 , pp. 949-982
    • Constantin, A.1    McKean, H.2
  • 10
    • 0042279206 scopus 로고    scopus 로고
    • On the geometric approach to the motion of inertial mechanical systems
    • Constantin, A., Kolev, B.: On the geometric approach to the motion of inertial mechanical systems. J. Phys. A 35, R51-R79 (2002)
    • (2002) J. Phys. A , vol.35
    • Constantin, A.1    Kolev, B.2
  • 11
    • 0242350978 scopus 로고    scopus 로고
    • Geodesic flow on the diffeomorphism group of the circle
    • Constantin, A., Kolev, B.: Geodesic flow on the diffeomorphism group of the circle. Comment. Math. Helv. 78, 787-804 (2003)
    • (2003) Comment. Math. Helv , vol.78 , pp. 787-804
    • Constantin, A.1    Kolev, B.2
  • 12
    • 30644471049 scopus 로고    scopus 로고
    • Integrability of invariant metrics on the Virasoro group
    • Constantin, A., Kolev, B., Lenells, J.: Integrability of invariant metrics on the Virasoro group. Phys. Lett. A 350, 75-60 (2006)
    • (2006) Phys. Lett. A , vol.350 , pp. 75-60
    • Constantin, A.1    Kolev, B.2    Lenells, J.3
  • 13
    • 33847314226 scopus 로고    scopus 로고
    • De Lellis, C., Rappeler, T., Tbpalov, P.: Low regularity solutions of the Camassa-Holm equation (to appear in Comm. Partial Differential Equations)
    • De Lellis, C., Rappeler, T., Tbpalov, P.: Low regularity solutions of the Camassa-Holm equation (to appear in Comm. Partial Differential Equations)
  • 14
    • 33847303628 scopus 로고    scopus 로고
    • Deligne, P., Etingof, P.: Quantum Fields and Strings: a course for mathematicians, vols. 1 and 2. Amer. Math. Soc., Providence, RI; Institute for Advanced Study, Princeton, NJ (1999)
    • Deligne, P., Etingof, P.: Quantum Fields and Strings: a course for mathematicians, vols. 1 and 2. Amer. Math. Soc., Providence, RI; Institute for Advanced Study, Princeton, NJ (1999)
  • 15
    • 0001052255 scopus 로고
    • Groups of diffeomorphisms and the motion of an incompressible fluid
    • Ebin, D., Marsden, J.: Groups of diffeomorphisms and the motion of an incompressible fluid. Ann. Math. 92, 102-163 (1970)
    • (1970) Ann. Math , vol.92 , pp. 102-163
    • Ebin, D.1    Marsden, J.2
  • 16
    • 49049150360 scopus 로고
    • Symplectic structures, their Bäcklund transformation and hereditary symmetries
    • Fokas, A., Fuchssteiner, B.: Symplectic structures, their Bäcklund transformation and hereditary symmetries. Physica D 4, 47-66 (1981)
    • (1981) Physica D , vol.4 , pp. 47-66
    • Fokas, A.1    Fuchssteiner, B.2
  • 17
    • 84966236065 scopus 로고
    • The inverse function theorem of Nash and Moser
    • Hamilton, R.: The inverse function theorem of Nash and Moser. Bull. Amer. Math. Soc. 7, 66-222 (1982)
    • (1982) Bull. Amer. Math. Soc , vol.7 , pp. 66-222
    • Hamilton, R.1
  • 18
    • 0001971504 scopus 로고    scopus 로고
    • The Euler-Poincaré equations and semidirect products with applications to continuum theories
    • Holm, D., Marsden, J., Ratiu, T.: The Euler-Poincaré equations and semidirect products with applications to continuum theories. Adv. Math. 137, 1-81 (1998)
    • (1998) Adv. Math , vol.137 , pp. 1-81
    • Holm, D.1    Marsden, J.2    Ratiu, T.3
  • 19
    • 33847289805 scopus 로고    scopus 로고
    • Kappeier, T., Pöschel, J.: KdV&KAM. Springer-Verlag, Berlin (2003)
    • Kappeier, T., Pöschel, J.: KdV&KAM. Springer-Verlag, Berlin (2003)
  • 20
    • 33847287368 scopus 로고    scopus 로고
    • -1 (double struck T sign) (to appear in Duke Math. J.)
    • -1 (double struck T sign) (to appear in Duke Math. J.)
  • 21
    • 0016594542 scopus 로고
    • The Cauchy problem for quasi-linear symmetric hyperbolic systems
    • Kato, T.: The Cauchy problem for quasi-linear symmetric hyperbolic systems. Arch. Rational Mech. Anal. 58, 181-205 (1975)
    • (1975) Arch. Rational Mech. Anal , vol.58 , pp. 181-205
    • Kato, T.1
  • 22
    • 0037612018 scopus 로고    scopus 로고
    • Euler equations on homogeneous spaces and Virasoro orbits
    • Khesin, B., Misiolek, G.: Euler equations on homogeneous spaces and Virasoro orbits. Adv. Math. 176, 116-144 (2003)
    • (2003) Adv. Math , vol.176 , pp. 116-144
    • Khesin, B.1    Misiolek, G.2
  • 23
    • 0011879223 scopus 로고
    • Commuting diffeomorphisms
    • Amer. Math. Soc
    • Kopell, N.: Commuting diffeomorphisms. (Proc. Sympos. Pure Math). Amer. Math. Soc. 14, 165-184 (1970)
    • (1970) (Proc. Sympos. Pure Math) , vol.14 , pp. 165-184
    • Kopell, N.1
  • 24
    • 0033483085 scopus 로고    scopus 로고
    • The Camassa-Holm equation as a geodesic flow on the diffeomorphism group
    • Kouranbaeva, S.: The Camassa-Holm equation as a geodesic flow on the diffeomorphism group. J. Math. Phys. 40, 857-868 (1999)
    • (1999) J. Math. Phys , vol.40 , pp. 857-868
    • Kouranbaeva, S.1
  • 25
    • 33847266368 scopus 로고    scopus 로고
    • 24a. Kriegl, A., Michor, P.: The convenient setting of global analysis. Math. Surveys and Monographs, Amar. Math. Soc. 53 (1997)
    • 24a. Kriegl, A., Michor, P.: The convenient setting of global analysis. Math. Surveys and Monographs, Amar. Math. Soc. 53 (1997)
  • 27
    • 13244273595 scopus 로고    scopus 로고
    • The correspondence between KdV and Camassa-Holm
    • Lenells, J.: The correspondence between KdV and Camassa-Holm. Int. Math. Res. Not. 71, 3797-3811 (2004)
    • (2004) Int. Math. Res. Not , vol.71 , pp. 3797-3811
    • Lenells, J.1
  • 28
    • 2442552977 scopus 로고    scopus 로고
    • The Liouville correspondence between the Korteweg-de Vries and the Camassa-Holm hierarchies
    • McKean, H.P.: The Liouville correspondence between the Korteweg-de Vries and the Camassa-Holm hierarchies. Comm. Pure Appl. Math. 56, 998-1015 (2003)
    • (2003) Comm. Pure Appl. Math , vol.56 , pp. 998-1015
    • McKean, H.P.1
  • 29
    • 22444453467 scopus 로고    scopus 로고
    • On the geometry of the Virasoro-Bott group
    • Michor, P., Ratiu, T.: On the geometry of the Virasoro-Bott group. J. Lie Theory 8, 293-309 (1998)
    • (1998) J. Lie Theory , vol.8 , pp. 293-309
    • Michor, P.1    Ratiu, T.2
  • 30
    • 0001335921 scopus 로고
    • Remarks on infinite-dimensional Lie groups
    • Elsevier Science Publishers, Amsterdam
    • Milnor, J.: Remarks on infinite-dimensional Lie groups. Les Houches, Session XL, 1983, Elsevier Science Publishers, Amsterdam (1984)
    • (1984) Les Houches, Session XL, 1983
    • Milnor, J.1
  • 31
    • 0031989845 scopus 로고    scopus 로고
    • Misiolek, G.: A shallow water equation as a geodesic flow on the Bott-Virasoro group. I Geom. Phys. 24, 203-208 (1998)
    • Misiolek, G.: A shallow water equation as a geodesic flow on the Bott-Virasoro group. I Geom. Phys. 24, 203-208 (1998)
  • 32
    • 0036436154 scopus 로고    scopus 로고
    • Classical solutions of the periodic Camassa-Holm equation
    • Misiolek, G.: Classical solutions of the periodic Camassa-Holm equation. Geom. Funct. Anal. 12, 1080-1104 (2002)
    • (2002) Geom. Funct. Anal , vol.12 , pp. 1080-1104
    • Misiolek, G.1
  • 33
    • 34250093431 scopus 로고
    • Korteweg-de Vries superequations as an Euler equation
    • Ovsienko, V., Khesin, B.: Korteweg-de Vries superequations as an Euler equation. Funct. Anal. Appl. 21, 81-82 (1987)
    • (1987) Funct. Anal. Appl , vol.21 , pp. 81-82
    • Ovsienko, V.1    Khesin, B.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.