메뉴 건너뛰기




Volumn 17, Issue 1, 2017, Pages 127-159

The Lie Group Structure of the Butcher Group

Author keywords

Butcher group; Hopf algebra of rooted trees; Infinite dimensional Lie group; Regularity of Lie groups; Symplectic methods

Indexed keywords

ALGEBRA; DIFFERENTIAL EQUATIONS; FORESTRY; ORDINARY DIFFERENTIAL EQUATIONS; RUNGE KUTTA METHODS;

EID: 84947611040     PISSN: 16153375     EISSN: 16153383     Source Type: Journal    
DOI: 10.1007/s10208-015-9285-5     Document Type: Article
Times cited : (14)

References (30)
  • 1
    • 84947488504 scopus 로고    scopus 로고
    • Differentiable mappings on products with different degrees of differentiability in the two factors
    • H. Alzaareer and A. Schmeding. Differentiable mappings on products with different degrees of differentiability in the two factors. Expositiones Mathematicae, (33):184–222, 2015. doi:10.1016/j.exmath.2014.07.002.
    • (2015) Expositiones Mathematicae , vol.33 , pp. 184-222
    • Alzaareer, H.1    Schmeding, A.2
  • 2
    • 51249170322 scopus 로고
    • Applications différentiables et variétés différentiables de dimension infinie
    • A. Bastiani. Applications différentiables et variétés différentiables de dimension infinie. J. Analyse Math., 13:1–114, 1964.
    • (1964) J. Analyse Math. , vol.13 , pp. 1-114
    • Bastiani, A.1
  • 3
    • 85010853662 scopus 로고    scopus 로고
    • Character groups of Hopf algebras as infinite-dimensional Lie groups
    • G. Bogfjellmo, R. Dahmen, and A. Schmeding. Character groups of Hopf algebras as infinite-dimensional Lie groups. arXiv:1501.05221v3, Apr. 2015.
    • (2015) arXiv:1501.05221v3
    • Bogfjellmo, G.1    Dahmen, R.2    Schmeding, A.3
  • 4
    • 8144231442 scopus 로고    scopus 로고
    • Trees, renormalization and differential equations
    • C. Brouder. Trees, renormalization and differential equations. BIT Num. Anal., 44:425–438, 2004.
    • (2004) BIT Num. Anal. , vol.44 , pp. 425-438
    • Brouder, C.1
  • 5
    • 84968481790 scopus 로고
    • An algebraic theory of integration methods
    • J. C. Butcher. An algebraic theory of integration methods. Math. Comp., 26:79–106, 1972.
    • (1972) Math. Comp. , vol.26 , pp. 79-106
    • Butcher, J.C.1
  • 6
    • 85010897940 scopus 로고    scopus 로고
    • M. P. Calvo, A. Murua, and J. M. Sanz-Serna. Modified equations for ODEs. In Chaotic numerics (Geelong, 1993), volume 172 of Contemp. Math., pages 63–74. Amer. Math. Soc., Providence, RI, 1994.
    • M. P. Calvo, A. Murua, and J. M. Sanz-Serna. Modified equations for ODEs. In Chaotic numerics (Geelong, 1993), volume 172 of Contemp. Math., pages 63–74. Amer. Math. Soc., Providence, RI, 1994.
  • 7
    • 21344498105 scopus 로고
    • Canonical B-series
    • M. P. Calvo and J. M. Sanz-Serna. Canonical B-series. Numer. Math., 67(2):161–175, 1994.
    • (1994) Numer. Math. , vol.67 , Issue.2 , pp. 161-175
    • Calvo, M.P.1    Sanz-Serna, J.M.2
  • 9
    • 84864302262 scopus 로고    scopus 로고
    • Higher-order averaging, formal series and numerical integration II: The quasi-periodic case
    • P. Chartier, A. Murua, and J. M. Sanz-Serna. Higher-order averaging, formal series and numerical integration II: The quasi-periodic case. Found. Comput. Math., 12(4):471–508, 2012.
    • (2012) Found. Comput. Math. , vol.12 , Issue.4 , pp. 471-508
    • Chartier, P.1    Murua, A.2    Sanz-Serna, J.M.3
  • 10
    • 0032257297 scopus 로고    scopus 로고
    • Hopf Algebras, Renormalization and Noncommutative Geometry
    • A. Connes and D. Kreimer. Hopf Algebras, Renormalization and Noncommutative Geometry. Commun.Math.Phys. 199 203–242, 1998.
    • (1998) Commun. Math. Phys. , vol.199 , pp. 203-242
    • Connes, A.1    Kreimer, D.2
  • 11
    • 84869157914 scopus 로고    scopus 로고
    • Direct Limit Constructions in Infinite Dimensional Lie Theory. PhD thesis
    • R. Dahmen. Direct Limit Constructions in Infinite Dimensional Lie Theory. PhD thesis, University of Paderborn, 2011. urn:nbn:de:hbz:466:2-239.
    • University of Paderborn, 2011. urn:nbn:de:hbz , vol.466 , pp. 2-239
    • Dahmen, R.1
  • 14
    • 0036808583 scopus 로고    scopus 로고
    • Lie group structures on quotient groups and universal complexifications for infinite-dimensional Lie groups
    • H. Glöckner. Lie group structures on quotient groups and universal complexifications for infinite-dimensional Lie groups. J. Funct. Anal., 194(2):347–409, 2002.
    • (2002) J. Funct. Anal. , vol.194 , Issue.2 , pp. 347-409
    • Glöckner, H.1
  • 15
    • 41149170598 scopus 로고    scopus 로고
    • Instructive examples of smooth, complex differentiable and complex analytic mappings into locally convex spaces
    • H. Glöckner. Instructive examples of smooth, complex differentiable and complex analytic mappings into locally convex spaces. J. Math. Kyoto Univ., 47(3):631–642, 2007.
    • (2007) J. Math. Kyoto Univ. , vol.47 , Issue.3 , pp. 631-642
    • Glöckner, H.1
  • 16
    • 85010868038 scopus 로고    scopus 로고
    • Regularity properties of infinite-dimensional Lie groups, and semiregularity
    • H. Glöckner. Regularity properties of infinite-dimensional Lie groups, and semiregularity. arXiv:1208.0715v3, Jan. 2015.
    • (2015) arXiv:1208.0715v3
    • Glöckner, H.1
  • 17
    • 85010894108 scopus 로고    scopus 로고
    • H. Glöckner. Infinite-dimensional Lie groups without completeness restrictions. In A. Strasburger, J. Hilgert, K. Neeb, and W. Wojtyński, editors, Geometry and Analysis on Lie Groups, volume 55 of Banach Center Publication, pages 43–59. Warsaw, 2002.
    • H. Glöckner. Infinite-dimensional Lie groups without completeness restrictions. In A. Strasburger, J. Hilgert, K. Neeb, and W. Wojtyński, editors, Geometry and Analysis on Lie Groups, volume 55 of Banach Center Publication, pages 43–59. Warsaw, 2002.
  • 18
    • 84963041997 scopus 로고
    • Locally unbounded topological fields and box topologies on products of vector spaces
    • G. G. Gould. Locally unbounded topological fields and box topologies on products of vector spaces. J. London Math. Soc., 36:273–281, 1961.
    • (1961) J. London Math. Soc. , vol.36 , pp. 273-281
    • Gould, G.G.1
  • 19
    • 0031505057 scopus 로고    scopus 로고
    • The life-span of backward error analysis for numerical integrators
    • E. Hairer and C. Lubich. The life-span of backward error analysis for numerical integrators. Numerische Mathematik, 76(4):441–462, 1997.
    • (1997) Numerische Mathematik , vol.76 , Issue.4 , pp. 441-462
    • Hairer, E.1    Lubich, C.2
  • 20
    • 85010888489 scopus 로고    scopus 로고
    • 2 2006.
    • 2 2006.
  • 21
    • 0003996158 scopus 로고
    • Locally Convex Spaces
    • Teubner, Stuttgart
    • H. Jarchow. Locally Convex Spaces. Lecture Notes in Mathematics 417. Teubner, Stuttgart, 1981.
    • (1981) Lecture Notes in Mathematics , vol.417
    • Jarchow, H.1
  • 22
    • 0003235678 scopus 로고
    • Differential Calculus in Locally Convex Spaces
    • Springer Verlag, Berlin
    • H. Keller. Differential Calculus in Locally Convex Spaces. Lecture Notes in Mathematics 417. Springer Verlag, Berlin, 1974.
    • (1974) Lecture Notes in Mathematics , vol.417
    • Keller, H.1
  • 24
    • 0003023917 scopus 로고    scopus 로고
    • The convenient setting of global analysis, volume 53 of Mathematical Surveys and Monographs
    • A. Kriegl and P. W. Michor. The convenient setting of global analysis, volume 53 of Mathematical Surveys and Monographs. AMS, 1997.
    • (1997) AMS
    • Kriegl, A.1    Michor, P.W.2
  • 27
    • 0003626553 scopus 로고
    • Manifolds of Differentiable Mappings
    • Shiva Publishing Ltd., Orpington
    • P. Michor. Manifolds of Differentiable Mappings. Shiva Mathematics Series 3. Shiva Publishing Ltd., Orpington, 1980.
    • (1980) Shiva Mathematics Series , vol.3
    • Michor, P.1
  • 28
    • 85010856522 scopus 로고    scopus 로고
    • J. Milnor. Remarks on infinite-dimensional Lie groups. In B. DeWitt and R. Stora, editors, Relativity, Groups and Topology II, pages 1007–1057. North Holland, New York, 1983.
    • J. Milnor. Remarks on infinite-dimensional Lie groups. In B. DeWitt and R. Stora, editors, Relativity, Groups and Topology II, pages 1007–1057. North Holland, New York, 1983.
  • 29
    • 33749023336 scopus 로고    scopus 로고
    • Towards a Lie theory of locally convex groups
    • K. Neeb. Towards a Lie theory of locally convex groups. Japanese Journal of Mathematics, 1(2):291–468, 2006.
    • (2006) Japanese Journal of Mathematics , vol.1 , Issue.2 , pp. 291-468
    • Neeb, K.1
  • 30
    • 85010915039 scopus 로고
    • Third printing corrected
    • H. H. Schaefer. Topological vector spaces. Springer-Verlag, New York-Berlin, 1971. Third printing corrected, Graduate Texts in Mathematics, Vol. 3.
    • (1971) Graduate Texts in Mathematics , vol.3


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.