메뉴 건너뛰기




Volumn 31, Issue 36, 1998, Pages 7379-7402

Finding Lie groups that reduce the order of discrete dynamical systems

Author keywords

[No Author keywords available]

Indexed keywords


EID: 0032508449     PISSN: 03054470     EISSN: None     Source Type: Journal    
DOI: 10.1088/0305-4470/31/36/010     Document Type: Article
Times cited : (8)

References (54)
  • 10
    • 0003547445 scopus 로고
    • Encyclopedia of Mathematics Reading, MA: Addison-Wesley
    • Miller W 1977 Symmetry and Separation of Variables (Encyclopedia of Mathematics vol 4) (Reading, MA: Addison-Wesley)
    • (1977) Symmetry and Separation of Variables , vol.4
    • Miller, W.1
  • 12
    • 0001156359 scopus 로고
    • Canonical structure and symmetries for discrete systems
    • Maeda S 1980 Canonical structure and symmetries for discrete systems Math. Japonica 25 405
    • (1980) Math. Japonica , vol.25 , pp. 405
    • Maeda, S.1
  • 13
    • 0040639061 scopus 로고
    • Lie-point symmetries of discrete versus continuous dynamical systems
    • Gaeta G 1993 Lie-point symmetries of discrete versus continuous dynamical systems Phys. Lett. 178A 376
    • (1993) Phys. Lett. , vol.178 A , pp. 376
    • Gaeta, G.1
  • 16
    • 0001352348 scopus 로고
    • Embedded elliptic curves and the Yang-Baxter equation
    • Tracy C A 1985 Embedded elliptic curves and the Yang-Baxter equation Physica 16D 203
    • (1985) Physica , vol.16 D , pp. 203
    • Tracy, C.A.1
  • 18
    • 0000136587 scopus 로고
    • Rational mappings, arborescent iterations, and the symmetries of integrability
    • Bellon M P, Maillard J-M and Viallet C-M 1991 Rational mappings, arborescent iterations, and the symmetries of integrability Phys. Rev. Lett. 67 1373
    • (1991) Phys. Rev. Lett. , vol.67 , pp. 1373
    • Bellon, M.P.1    Maillard, J.-M.2    Viallet, C.-M.3
  • 21
    • 45449122562 scopus 로고
    • Symmetry increasing bifurcation of chaotic attractors
    • Chossat P and Golubitsky M 1988 Symmetry increasing bifurcation of chaotic attractors Physica 32D 423
    • (1988) Physica , vol.32 D , pp. 423
    • Chossat, P.1    Golubitsky, M.2
  • 23
    • 0028424585 scopus 로고
    • Transitivity of orbits of maps symmetric under compact Lie groups
    • Ashwin P, Chossat P and Stewart I 1994 Transitivity of orbits of maps symmetric under compact Lie groups Chaos, Solitons and Fractals 4 621
    • (1994) Chaos, Solitons and Fractals , vol.4 , pp. 621
    • Ashwin, P.1    Chossat, P.2    Stewart, I.3
  • 25
    • 4243673219 scopus 로고
    • Lie symmetries and the integration of difference equations
    • Quispel G and Sahadevan R 1993 Lie symmetries and the integration of difference equations Phys. Lett. 184A 64
    • (1993) Phys. Lett. , vol.184 A , pp. 64
    • Quispel, G.1    Sahadevan, R.2
  • 26
    • 0000474920 scopus 로고
    • Factorizable Lie symmetries and the linearization of difference equations
    • Byrnes G B, Sahadevan R and Quispel G 1995 Factorizable Lie symmetries and the linearization of difference equations Nonlinearity 8 443
    • (1995) Nonlinearity , vol.8 , pp. 443
    • Byrnes, G.B.1    Sahadevan, R.2    Quispel, G.3
  • 27
    • 0039975457 scopus 로고    scopus 로고
    • Lie groups and solution of dynamical problems on fractal lattices
    • ed M Novak and T Dewey (Pine Brook, NJ: World Scientific)
    • Schwalm W, Schwalm M and Giona M 1997 Lie groups and solution of dynamical problems on fractal lattices Fractal Frontiers ed M Novak and T Dewey (Pine Brook, NJ: World Scientific)
    • (1997) Fractal Frontiers
    • Schwalm, W.1    Schwalm, M.2    Giona, M.3
  • 28
    • 0040568298 scopus 로고    scopus 로고
    • Group theoretic reduction of Laplacian dynamical problems on fractal lattices
    • Schwalm W, Schwalm M and Giona M 1997 Group theoretic reduction of Laplacian dynamical problems on fractal lattices Phys. Rev. E 55 6741
    • (1997) Phys. Rev. E , vol.55 , pp. 6741
    • Schwalm, W.1    Schwalm, M.2    Giona, M.3
  • 29
    • 0039975458 scopus 로고    scopus 로고
    • Group theoretic reduction of discrete diffusion equations on regular fractal structures
    • ed M Giona and G Biardi (Singapore: World Scientific)
    • Schwalm W, Schwalm M and Giona M 1997 Group theoretic reduction of discrete diffusion equations on regular fractal structures Proc. CFIC 1996: Fractals and Chaos in Chemical Engineering ed M Giona and G Biardi (Singapore: World Scientific)
    • (1997) Proc. CFIC 1996: Fractals and Chaos in Chemical Engineering
    • Schwalm, W.1    Schwalm, M.2    Giona, M.3
  • 30
    • 0030267265 scopus 로고    scopus 로고
    • Exact solution of linear transport equations in fractal media - I. Renormalization analysis and general theory
    • Giona M, Schwalm W, Schwalm M and Adrover A 1996 Exact solution of linear transport equations in fractal media - I. Renormalization analysis and general theory Chem. Eng. Sci. 51 4717
    • (1996) Chem. Eng. Sci. , vol.51 , pp. 4717
    • Giona, M.1    Schwalm, W.2    Schwalm, M.3    Adrover, A.4
  • 31
    • 0030268143 scopus 로고    scopus 로고
    • Exact solution of linear transport equations in fractal media - II. Diffusion and convection
    • Giona M, Schwalm W, Schwalm M and Adrover A 1996 Exact solution of linear transport equations in fractal media - II. Diffusion and convection Chem. Eng. Sci. 51 4731
    • (1996) Chem. Eng. Sci. , vol.51 , pp. 4731
    • Giona, M.1    Schwalm, W.2    Schwalm, M.3    Adrover, A.4
  • 32
    • 0030579948 scopus 로고    scopus 로고
    • Exact solution of linear transport equations in fractal media - III. Adsorption and chemical reaction
    • Giona M, Schwalm W, Schwalm M and Adrover A 1996 Exact solution of linear transport equations in fractal media - III. Adsorption and chemical reaction Chem. Eng. Sci. 51 5065
    • (1996) Chem. Eng. Sci. , vol.51 , pp. 5065
    • Giona, M.1    Schwalm, W.2    Schwalm, M.3    Adrover, A.4
  • 34
    • 0041162433 scopus 로고
    • American Mathematical Society Regional Conf. Series No 37 (Providence, RI: American Mathematical Society)
    • Nagata M 1977 Polynomial Rings and Affine Spaces (American Mathematical Society Regional Conf. Series No 37) (Providence, RI: American Mathematical Society)
    • (1977) Polynomial Rings and Affine Spaces
    • Nagata, M.1
  • 37
    • 0009005969 scopus 로고
    • Integrable mappings and polynomial growth
    • Boukra S. Maillard J-M and Rollet G 1994 Integrable mappings and polynomial growth Physica 209A 162
    • (1994) Physica , vol.209 A , pp. 162
    • Boukra, S.1    Maillard, J.-M.2    Rollet, G.3
  • 38
    • 0007230746 scopus 로고
    • Factorization properties of birational mappings
    • Boukraa S and Maillard J-M 1995 Factorization properties of birational mappings Physica 220A 403
    • (1995) Physica , vol.220 A , pp. 403
    • Boukraa, S.1    Maillard, J.-M.2
  • 40
    • 0031166110 scopus 로고    scopus 로고
    • New integrable cases of a Cremona transformation: A finite-order orbits analysis
    • Boukraa S, Hassani S and J-M Maillard 1997 New integrable cases of a Cremona transformation: a finite-order orbits analysis Physica 240A 586
    • (1997) Physica , vol.240 A , pp. 586
    • Boukraa, S.1    Hassani, S.2    Maillard, J.-M.3
  • 41
    • 0000964819 scopus 로고
    • Growth and integrability in the dynamics of mappings
    • Veselov A 1992 Growth and integrability in the dynamics of mappings Commun. Math. Phys. 145 181
    • (1992) Commun. Math. Phys. , vol.145 , pp. 181
    • Veselov, A.1
  • 44
    • 0001996738 scopus 로고
    • Dynamics of intersections
    • Research Papers Published in Honor of J Moser's 60th Birthday ed P Rabinowitz and E Zehnder (New York: Academic)
    • Arnold V I 1990 Dynamics of intersections Analysis Et Cetera. Research Papers Published in Honor of J Moser's 60th Birthday ed P Rabinowitz and E Zehnder (New York: Academic)
    • (1990) Analysis Et Cetera
    • Arnold, V.I.1
  • 45
    • 0001001511 scopus 로고
    • Singularity, complexity and quasi-integrability of rational mappings
    • Viallet C M and Falqui G 1993 Singularity, complexity and quasi-integrability of rational mappings Commun. Math. Phys. 154 111
    • (1993) Commun. Math. Phys. , vol.154 , pp. 111
    • Viallet, C.M.1    Falqui, G.2
  • 47
    • 0040568297 scopus 로고    scopus 로고
    • Scaling and scaling crossover for transport on anisotropic structures
    • Adrover A, Schwalm W, Giona M and Bachand D 1997 Scaling and scaling crossover for transport on anisotropic structures Phys. Rev. E 55 7304
    • (1997) Phys. Rev. E , vol.55 , pp. 7304
    • Adrover, A.1    Schwalm, W.2    Giona, M.3    Bachand, D.4
  • 48
    • 0006357704 scopus 로고
    • Fractal models for diffusion controlled aggregation
    • Vicsek T 1983 Fractal models for diffusion controlled aggregation J. Phys. A: Math Gen. 16 L647
    • (1983) J. Phys. A: Math Gen. , vol.16
    • Vicsek, T.1
  • 49
    • 0039915169 scopus 로고
    • Dynamics of a Vicsek fractal: The boundary effect and the interplay among the local symmetry, the self-similarity, and the structure of the fractal
    • Jayanthi C S and Wu S Y 1994 Dynamics of a Vicsek fractal: the boundary effect and the interplay among the local symmetry, the self-similarity, and the structure of the fractal Phys. Rev. B 50 897
    • (1994) Phys. Rev. B , vol.50 , pp. 897
    • Jayanthi, C.S.1    Wu, S.Y.2
  • 50
    • 0041162422 scopus 로고    scopus 로고
    • Diffusion of material and energy on Vicsek and related lattices
    • ed M Giona and G Biardi (Singapore: World Scientific)
    • Schwalm M, Ni H and Ludlow D 1997 Diffusion of material and energy on Vicsek and related lattices Proc. CFIC 1996: Fractals and Chaos in Chemical Engineering ed M Giona and G Biardi (Singapore: World Scientific)
    • (1997) Proc. CFIC 1996: Fractals and Chaos in Chemical Engineering
    • Schwalm, M.1    Ni, H.2    Ludlow, D.3
  • 51
    • 0041162424 scopus 로고
    • Density of states of a sierpiński gasket in two dimensions with anisotropic interactions
    • Hood M and Southern B W 1986 Density of states of a Sierpiński gasket in two dimensions with anisotropic interactions J. Phys. A: Math Gen. 19 2679
    • (1986) J. Phys. A: Math Gen. , vol.19 , pp. 2679
    • Hood, M.1    Southern, B.W.2
  • 52
    • 36749120733 scopus 로고
    • Self-avoiding random walks: Some exactly soluble cases
    • Dhar D 1977 Self-avoiding random walks: some exactly soluble cases J. Math Phys. 19 5
    • (1977) J. Math Phys. , vol.19 , pp. 5
    • Dhar, D.1
  • 54
    • 0011379512 scopus 로고
    • Some properties of the spectrum of the sierpiński gasket in a magnetic field
    • Alexander S 1984 Some properties of the spectrum of the Sierpiński gasket in a magnetic field Phys. Rev. B 29 5504
    • (1984) Phys. Rev. B , vol.29 , pp. 5504
    • Alexander, S.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.