메뉴 건너뛰기




Volumn 39, Issue 5, 1998, Pages 2929-2946

Algebraic structures and invariant manifolds of differential systems

Author keywords

[No Author keywords available]

Indexed keywords


EID: 0032371704     PISSN: 00222488     EISSN: None     Source Type: Journal    
DOI: 10.1063/1.532429     Document Type: Article
Times cited : (35)

References (36)
  • 1
    • 51249180884 scopus 로고
    • Nonlinear evolutions equations and ordinary differential equations of Painlevé type
    • M. J. Ablowitz, A. Ramani, and H. Segur, "Nonlinear evolutions equations and ordinary differential equations of Painlevé type," Lett. Nuovo Cimento 23, 333-338 (1978).
    • (1978) Lett. Nuovo Cimento , vol.23 , pp. 333-338
    • Ablowitz, M.J.1    Ramani, A.2    Segur, H.3
  • 2
    • 36749106124 scopus 로고
    • A connexion between nonlinear evolution equations and ordinary differential equations of P-type I
    • M. J. Ablowitz, A. Ramani, and H. Segur, "A connexion between nonlinear evolution equations and ordinary differential equations of P-type I," J. Math. Phys. 21, 715-721 (1930).
    • (1930) J. Math. Phys. , vol.21 , pp. 715-721
    • Ablowitz, M.J.1    Ramani, A.2    Segur, H.3
  • 3
    • 45349111974 scopus 로고
    • The Painlevé property and singularity analysis of integrable and non-integrable systems
    • A. Ramani, B. Grammaticos, and T. Bountis, "The Painlevé property and singularity analysis of integrable and non-integrable systems." Phys. Rep. 180, 159-245 (1990).
    • (1990) Phys. Rep. , vol.180 , pp. 159-245
    • Ramani, A.1    Grammaticos, B.2    Bountis, T.3
  • 4
    • 48549109270 scopus 로고
    • On the complete and partial integrability of non-Hamiltonian systems
    • T. Bountis, A. Ramani, B. Grammaticos, and B. Dorizzi, "On the complete and partial integrability of non-Hamiltonian systems," Physica A 128, 268-288 (1984).
    • (1984) Physica A , vol.128 , pp. 268-288
    • Bountis, T.1    Ramani, A.2    Grammaticos, B.3    Dorizzi, B.4
  • 5
    • 0003842982 scopus 로고
    • unter Milwirkung von F. Engel Teubner, Leipzig
    • S. Lie, "Theorie der Transformationgruppen," unter Milwirkung von F. Engel (Teubner, Leipzig, 1893), Vols. 1-3.
    • (1893) Theorie der Transformationgruppen , vol.1-3
    • Lie, S.1
  • 6
    • 0002063211 scopus 로고
    • Differential equations form the group standpoints
    • L. E. Dixon, "Differential equations form the group standpoints," Ann. Math. 25(1), 287-378 (1924).
    • (1924) Ann. Math. , vol.25 , Issue.1 , pp. 287-378
    • Dixon, L.E.1
  • 7
    • 0003345224 scopus 로고
    • Applications of Lie groups to differential equations
    • Springer Verlag, New York
    • P. J. Olver, Applications of Lie groups to differential equations, Graduate Text in Mathematics 107 (Springer Verlag, New York, 1986).
    • (1986) Graduate Text in Mathematics , vol.107
    • Olver, P.J.1
  • 8
    • 0024070164 scopus 로고
    • Simmetries of differential equations: From Sophus Lie to computer algebra
    • F. Schwartz, "Simmetries of differential equations: from Sophus Lie to computer algebra," SIAM (Soc. Ind. Appl. Math.) Rev. 30, 450-481 (1988).
    • (1988) SIAM (Soc. Ind. Appl. Math.) Rev. , vol.30 , pp. 450-481
    • Schwartz, F.1
  • 9
    • 0000983537 scopus 로고
    • A method of finding integrals for 3-dimensional dynamical systems
    • J. M. Strelcyn and S. Wojciechowski, "A method of finding integrals for 3-dimensional dynamical systems," Phys. Lett. A 133, 207-212 (1988).
    • (1988) Phys. Lett. A , vol.133 , pp. 207-212
    • Strelcyn, J.M.1    Wojciechowski, S.2
  • 10
    • 0001537866 scopus 로고
    • Quadratic differential equations and non-associative algebras
    • edited by L. Cesari, J. P. La Salle, and S. Lefshetz Princeton U.P. Princeton, NJ
    • L. Markus, "Quadratic differential equations and non-associative algebras," in Contributions to the Theory of Nonlinear Oscillations, edited by L. Cesari, J. P. La Salle, and S. Lefshetz (Princeton U.P. Princeton, NJ, 1960), Vol. 5, pp. 185-213.
    • (1960) Contributions to the Theory of Nonlinear Oscillations , vol.5 , pp. 185-213
    • Markus, L.1
  • 11
    • 49249151623 scopus 로고
    • Non associative real algebras and quadratic differential equations
    • J. Kaplan and J. Yorke, "Non associative real algebras and quadratic differential equations," Nonlinear Anal. TMA, 3, 49-51 (1979).
    • (1979) Nonlinear Anal. TMA , vol.3 , pp. 49-51
    • Kaplan, J.1    Yorke, J.2
  • 12
    • 0002122452 scopus 로고
    • Algebras and differential equations
    • H. Röhrl, "Algebras and differential equations," Nagoya Math. J. 68, 59-122 (1977).
    • (1977) Nagoya Math. J. , vol.68 , pp. 59-122
    • Röhrl, H.1
  • 13
    • 0011130334 scopus 로고
    • A theorem on non-associative algebras and its application to differential equations
    • H. Röhrl, "A theorem on non-associative algebras and its application to differential equations," Manuscr. Math. 21, 181-187 (1977).
    • (1977) Manuscr. Math. , vol.21 , pp. 181-187
    • Röhrl, H.1
  • 15
    • 0000124854 scopus 로고
    • Universal canonical forms for the time-continuous dynamical systems
    • L. Brenig and A. Goriely, "Universal canonical forms for the time-continuous dynamical systems," Phys. Rev. A 40(7), 4119-4122 (1989).
    • (1989) Phys. Rev. A , vol.40 , Issue.7 , pp. 4119-4122
    • Brenig, L.1    Goriely, A.2
  • 16
    • 0001967019 scopus 로고
    • Painlevé Analysis and Normal Forms
    • edited by E. Tournier Cambridge U.P., Cambridge
    • L. Brenig and A. Goriely, "Painlevé Analysis and Normal Forms," in London Math. Soc. Lecture Note Series 195, edited by E. Tournier (Cambridge U.P., Cambridge, 1994), pp. 211-237.
    • (1994) London Math. Soc. Lecture Note Series , vol.195 , pp. 211-237
    • Brenig, L.1    Goriely, A.2
  • 17
    • 0039361967 scopus 로고
    • Nonpolynomial vector fields under Lotka-Volterra normal form
    • B. Hernándes-Bermejo and V. Fairen, "Nonpolynomial vector fields under Lotka-Volterra normal form," Phys. Lett. A 206(1,2), 31-37 (1995).
    • (1995) Phys. Lett. A , vol.206 , Issue.1-2 , pp. 31-37
    • Hernándes-Bermejo, B.1    Fairen, V.2
  • 18
    • 0041160421 scopus 로고
    • Transformation of polynomial differential systems in the positive orthant
    • Sophia-Antilopis, 06561, Valbonne, France
    • J. L. Gouzé, "Transformation of polynomial differential systems in the positive orthant," Rapport INRIA, Sophia-Antilopis, 06561, Valbonne, France (1990).
    • (1990) Rapport INRIA
    • Gouzé, J.L.1
  • 19
    • 0022687590 scopus 로고
    • Equivalence between S-systems and Volterra systems
    • E. O. Voit and M. A. Savageau, "Equivalence between S-systems and Volterra systems," Math. Biosci. 78, 47-55 (1986).
    • (1986) Math. Biosci. , vol.78 , pp. 47-55
    • Voit, E.O.1    Savageau, M.A.2
  • 20
    • 85033938445 scopus 로고    scopus 로고
    • Lotka-Volterra representations of general nonlinear systems
    • in press
    • B. Hernándes-Bermejo and V. Fairén, "Lotka-Volterra representations of general nonlinear systems," Math. Biosci. (in press).
    • Math. Biosci.
    • Hernándes-Bermejo, B.1    Fairén, V.2
  • 21
    • 36749109668 scopus 로고
    • Universal formats for nonlinear ordinary differential systems
    • H. E. Kerner, "Universal formats for nonlinear ordinary differential systems," J. Math. Phys. 22, 1366-1371 (1981).
    • (1981) J. Math. Phys. , vol.22 , pp. 1366-1371
    • Kerner, H.E.1
  • 22
    • 0342349799 scopus 로고
    • Recasting nonlinear differential equations as S-systems: A canonical nonlinear form
    • M. A. Savageau and E. O. Voit, "Recasting nonlinear differential equations as S-systems: a canonical nonlinear form," Math. Biosci. 87, 83-115 (1987).
    • (1987) Math. Biosci. , vol.87 , pp. 83-115
    • Savageau, M.A.1    Voit, E.O.2
  • 23
    • 0001620238 scopus 로고
    • Analytical note on certain rhythmic relations in organic systems
    • A. J. Lotka, "Analytical note on certain rhythmic relations in organic systems," Proc. Natl. Acad. Sci. USA 6, 410 (1920).
    • (1920) Proc. Natl. Acad. Sci. USA , vol.6 , pp. 410
    • Lotka, A.J.1
  • 25
    • 0002144503 scopus 로고
    • Quadratical differential systems for interactive populations models
    • R. D. Jenks, "Quadratical differential systems for interactive populations models," J. Diff. Eqns. 5, 497-514 (1969).
    • (1969) J. Diff. Eqns. , vol.5 , pp. 497-514
    • Jenks, R.D.1
  • 26
    • 0042981278 scopus 로고
    • Commutative nonassociative algebras and cubic forms
    • D. K. Harrison, "Commutative nonassociative algebras and cubic forms," J. Algebra. 32, 518-528 (1974).
    • (1974) J. Algebra , vol.32 , pp. 518-528
    • Harrison, D.K.1
  • 29
    • 0001569894 scopus 로고
    • Families of invariants of the motion for the Lotka-Volterra equations: The linear polynomials family
    • L. Cairo and M. R. Feix, "Families of invariants of the motion for the Lotka-Volterra equations: the linear polynomials family," J. Math. Phys. 33, 2440-2455 (1992).
    • (1992) J. Math. Phys. , vol.33 , pp. 2440-2455
    • Cairo, L.1    Feix, M.R.2
  • 30
    • 0000241853 scopus 로고
    • Deterministic nonperiodic flow
    • E. N. Lorenz, "Deterministic nonperiodic flow," J. Atmos. Sci. 20, 130-141 (1963).
    • (1963) J. Atmos. Sci. , vol.20 , pp. 130-141
    • Lorenz, E.N.1
  • 31
    • 0000587469 scopus 로고
    • Lie symmetries of the Lorenz model
    • T. Sen and M. Tabor, "Lie symmetries of the Lorenz model," Physica D 44, 313-339 (1990).
    • (1990) Physica D , vol.44 , pp. 313-339
    • Sen, T.1    Tabor, M.2
  • 32
    • 0030355465 scopus 로고    scopus 로고
    • A geometrical method towards first integrals for dynamical systems
    • S. Labrunie and R. Conte, "A geometrical method towards first integrals for dynamical systems," J. Math. Phys. 37, 6198-6206 (1996).
    • (1996) J. Math. Phys. , vol.37 , pp. 6198-6206
    • Labrunie, S.1    Conte, R.2
  • 33
    • 21344483099 scopus 로고
    • Time-independent invariants of motion for the quadratic system
    • D. D. Hua, L. Cairo, and M. R. Feix, "Time-independent invariants of motion for the quadratic system," J. Phys. A 26, 7097-7114 (1993).
    • (1993) J. Phys. A , vol.26 , pp. 7097-7114
    • Hua, D.D.1    Cairo, L.2    Feix, M.R.3
  • 36
    • 48549109270 scopus 로고
    • On the complete and partial integrability of non-Hamiltonian systems
    • T. C. Bountis, A. Ramani, B Grammaticos, and B. Dorizzi. "On the complete and partial integrability of non-Hamiltonian systems," Physica A 128, 268-288 (1984).
    • (1984) Physica A , vol.128 , pp. 268-288
    • Bountis, T.C.1    Ramani, A.2    Grammaticos, B.3    Dorizzi, B.4


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.