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Volumn 264, Issue 1-2, 1999, Pages 264-293

Rational dynamical zeta functions for birational transformations

Author keywords

05.45.+b; 47.52.+j; Arnold complexity; Birational mappings; Cremona transformations; Discrete dynamical systems; Rational dynamical zeta functions; Topological entropy

Indexed keywords

MATHEMATICAL TRANSFORMATIONS; TOPOLOGY;

EID: 0033076417     PISSN: 03784371     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0378-4371(98)00452-X     Document Type: Article
Times cited : (22)

References (56)
  • 1
  • 3
    • 0001450585 scopus 로고
    • A new metric invariant of transitive dynamical systems and automorphisms in Lebesgue space
    • Kolmogorov A.N. A new metric invariant of transitive dynamical systems and automorphisms in Lebesgue space. Dokl. Acad. Nauk SSSR. 119:1958;861.
    • (1958) Dokl. Acad. Nauk SSSR , vol.119 , pp. 861
    • Kolmogorov, A.N.1
  • 4
    • 0000419815 scopus 로고
    • On the concept of entropy of dynamical system
    • Sinai YA.G. On the concept of entropy of dynamical system. Dokl. Acad. Nauk SSSR. 124:1959;768.
    • (1959) Dokl. Acad. Nauk SSSR , vol.124 , pp. 768
    • Sinai, Y.G.1
  • 6
    • 0007109184 scopus 로고
    • Problems on singularities and dynamical systems
    • in: V. Arnold, M. Monastyrsky (Eds.), Ch. 7
    • V. Arnold, Problems on singularities and dynamical systems, in: V. Arnold, M. Monastyrsky (Eds.), Developments in Mathematics: The Moscow School Chapman & Hall, Ch. 7, 1989, pp. 261-274.
    • (1989) Developments in Mathematics: The Moscow School Chapman & Hall , pp. 261-274
    • Arnold, V.1
  • 7
    • 48549112428 scopus 로고
    • Dimensions and entropies of strange attractors from a fluctuating dynamics approach
    • Grassberger P., Procaccia I. Dimensions and entropies of strange attractors from a fluctuating dynamics approach. Physica. 13 D:1984;34.
    • (1984) Physica , vol.13 D , pp. 34
    • Grassberger, P.1    Procaccia, I.2
  • 8
    • 35949018382 scopus 로고
    • Ergodic theory of chaos and strange attractors
    • Eckmann J.P., Ruelle D. Ergodic theory of chaos and strange attractors. Rev. Mod. Phys. 57:1985;617.
    • (1985) Rev. Mod. Phys. , vol.57 , pp. 617
    • Eckmann, J.P.1    Ruelle, D.2
  • 9
    • 0001816458 scopus 로고
    • Quantitative universality for a class of nonlinear transformations
    • Feigenbaum M.J. Quantitative universality for a class of nonlinear transformations. J. Stat. Phys. 19:1978;25.
    • (1978) J. Stat. Phys. , vol.19 , pp. 25
    • Feigenbaum, M.J.1
  • 10
  • 11
    • 0346372923 scopus 로고
    • The infinite number of generalized dimensions of fractals and strange attractors
    • Hentschel H.G.E., Procaccia I. The infinite number of generalized dimensions of fractals and strange attractors. Physica. 8 A:1983;435.
    • (1983) Physica , vol.8 , pp. 435
    • Hentschel, H.G.E.1    Procaccia, I.2
  • 12
    • 48549112428 scopus 로고
    • Dimensions and entropies of strange attractors from fluctuating dynamics approach
    • Grassberger P., Procaccia I. Dimensions and entropies of strange attractors from fluctuating dynamics approach. Physica. 13 D:1984;34.
    • (1984) Physica , vol.13 D , pp. 34
    • Grassberger, P.1    Procaccia, I.2
  • 13
    • 0001640825 scopus 로고
    • in: H.O. Peitgen, H.O. Walten (Eds.), Springer, Berlin
    • J.L. Kaplan, J.A. Yorke, in: H.O. Peitgen, H.O. Walten (Eds.), Lecture Notes in Math, vol. 730, Springer, Berlin, 1978, p. 228.
    • (1978) Lecture Notes in Math , vol.730 , pp. 228
    • Kaplan, J.L.1    Yorke, J.A.2
  • 14
    • 34250238889 scopus 로고
    • Some relations between dimension and Lyapounov exponents
    • Ledrappier F. Some relations between dimension and Lyapounov exponents. Comm. Math. Phys. 81:1981;229.
    • (1981) Comm. Math. Phys. , vol.81 , pp. 229
    • Ledrappier, F.1
  • 15
    • 0000241853 scopus 로고
    • Deterministic nonperiodic flow
    • Lorentz E. Deterministic nonperiodic flow. J. Atmos. Sci. 20:1963;130.
    • (1963) J. Atmos. Sci. , vol.20 , pp. 130
    • Lorentz, E.1
  • 16
    • 48749145669 scopus 로고
    • The dimension of chaotic attractors
    • Farmer J.D., Ott E., Yorke J.A. The dimension of chaotic attractors. Physica. 7 D:1983;153.
    • (1983) Physica , vol.7500 , pp. 153
    • Farmer, J.D.1    Ott, E.2    Yorke, J.A.3
  • 17
    • 0017185443 scopus 로고
    • Simple mathematical models with very complicated dynamic
    • May R.M. Simple mathematical models with very complicated dynamic. Nature. 261:1976;459.
    • (1976) Nature , vol.261 , pp. 459
    • May, R.M.1
  • 18
    • 0002591468 scopus 로고
    • A two-dimensional mapping with a strange attractor
    • Hénon H. A two-dimensional mapping with a strange attractor. Comm. Math. Phys. 50:1976;69.
    • (1976) Comm. Math. Phys. , vol.50 , pp. 69
    • Hénon, H.1
  • 19
    • 21844505428 scopus 로고
    • Discrete symmetry groups of vertex models in statistical mechanics
    • Boukraa S., Maillard J-M., Rollet G. Discrete symmetry groups of vertex models in statistical mechanics. J. Stat. Phys. 78:1995;1195.
    • (1995) J. Stat. Phys. , vol.78 , pp. 1195
    • Boukraa, S.1    Maillard, J-M.2    Rollet, G.3
  • 20
    • 0007162904 scopus 로고
    • Integrable mappings and polynomial growth
    • Boukraa S., Maillard J-M., Rollet G. Integrable mappings and polynomial growth. Physica A. 208:1994;115.
    • (1994) Physica a , vol.208 , pp. 115
    • Boukraa, S.1    Maillard, J-M.2    Rollet, G.3
  • 22
    • 0001237185 scopus 로고
    • Cremona group and dynamical systems
    • Veselov A.P. Cremona group and dynamical systems. Mat. Zametki. 45:1989;118.
    • (1989) Mat. Zametki. , vol.45 , pp. 118
    • Veselov, A.P.1
  • 23
    • 0000008977 scopus 로고
    • Discrete versions of some classical integrable systems and factorization of matrix polynomials
    • Moser J., Veselov A.P. Discrete versions of some classical integrable systems and factorization of matrix polynomials. Comm. Math. Phys. 139:1991;217.
    • (1991) Comm. Math. Phys. , vol.139 , pp. 217
    • Moser, J.1    Veselov, A.P.2
  • 24
    • 0000964819 scopus 로고
    • Growth and integrability in the dynamics of mappings
    • Veselov A.P. Growth and integrability in the dynamics of mappings. Comm. Math. Phys. 145:1992;181.
    • (1992) Comm. Math. Phys. , vol.145 , pp. 181
    • Veselov, A.P.1
  • 26
    • 0031166110 scopus 로고    scopus 로고
    • New integrable cases of a Cremona transformation: A finite order orbit analysis
    • Boukraa S., Hassani S., Maillard J-M. New integrable cases of a Cremona transformation: a finite order orbit analysis. Physica A. 240:1997;586.
    • (1997) Physica a , vol.240 , pp. 586
    • Boukraa, S.1    Hassani, S.2    Maillard, J-M.3
  • 27
    • 0002869924 scopus 로고
    • On periodic points
    • Artin M., Mazur B. On periodic points. Ann. Math. 81:1965;82.
    • (1965) Ann. Math. , vol.81 , pp. 82
    • Artin, M.1    Mazur, B.2
  • 29
    • 0346443935 scopus 로고
    • Distribution of closed orbits for linear automorphisms of tori
    • M. Degli Esposti, S. Isola, Distribution of closed orbits for linear automorphisms of tori, Nonlinearity 8 (1995) 827.
    • (1995) Nonlinearity , vol.8 , pp. 827
    • Degli Esposti, M.1    Isola, S.2
  • 30
    • 0032377221 scopus 로고    scopus 로고
    • Periodic orbits and dynamical spectra, Ergod
    • Baladi V. Periodic orbits and dynamical spectra, Ergod. Theory Dyn. Systems. 18:1998;255.
    • (1998) Theory Dyn. Systems , vol.18 , pp. 255
    • Baladi, V.1
  • 31
    • 0000058449 scopus 로고
    • Symbolic dynamics for hyperbolic flows
    • Bowen R. Symbolic dynamics for hyperbolic flows. Amer. J. Math. 95:1973;429.
    • (1973) Amer. J. Math. , vol.95 , pp. 429
    • Bowen, R.1
  • 32
    • 85009367586 scopus 로고
    • Equilibrium States and the Ergodic Theory of Anosov Diffeomorphisms
    • Springer, Berlin
    • R. Bowen, Equilibrium States and the Ergodic Theory of Anosov Diffeomorphisms, Lecture Notes in Math., vol. 470, Springer, Berlin, 1975.
    • (1975) Lecture Notes in Math. , vol.470
    • Bowen, R.1
  • 34
    • 0039506301 scopus 로고
    • Dynamical zeta functions: Where do they come from and what are they good for?
    • D. Ruelle, Dynamical zeta functions: where do they come from and what are they good for? IHES Preprint, IHES / P / 91 / 56, 1991.
    • (1991) IHES Preprint, IHES / P / 91 / 56
    • Ruelle, D.1
  • 35
    • 84968514104 scopus 로고
    • Differentiable dynamical systems
    • Smale C. Differentiable dynamical systems. Bull. Amer. Math. Soc. 73:1967;747.
    • (1967) Bull. Amer. Math. Soc. , vol.73 , pp. 747
    • Smale, C.1
  • 36
    • 0008026045 scopus 로고    scopus 로고
    • Visualization of a Hyperbolic structure in Area preserving maps
    • Giorgilli A., Lazutkin V.F., Simo C. Visualization of a Hyperbolic structure in Area preserving maps. Regular Chaotic Dynamics. 2:1997;47.
    • (1997) Regular Chaotic Dynamics , vol.2 , pp. 47
    • Giorgilli, A.1    Lazutkin, V.F.2    Simo, C.3
  • 40
    • 0039506261 scopus 로고
    • Comment compter avec les fonctions zeta
    • Baladi V. Comment compter avec les fonctions zeta. Gazette des Mathématiciens. 47:1991;79.
    • (1991) Gazette des Mathématiciens , vol.47 , pp. 79
    • Baladi, V.1
  • 41
    • 0001570657 scopus 로고
    • Axiom A diffeomorphisms have rational zeta functions
    • Manning A. Axiom. A diffeomorphisms have rational zeta functions Bull. London. Math. Soc. 3:1971;215.
    • (1971) Bull. London. Math. Soc. , vol.3 , pp. 215
    • Manning, A.1
  • 42
    • 0038913623 scopus 로고
    • Rationality for isolated Expansive Sets
    • Fried D. Rationality for isolated Expansive Sets. Adv. Math. 65:1987;35.
    • (1987) Adv. Math. , vol.65 , pp. 35
    • Fried, D.1
  • 43
    • 84966222790 scopus 로고
    • Isolated invariant sets and isolated blocks
    • Conley C., Easton R. Isolated invariant sets and isolated blocks. Trans. Amer. Math. Soc. 158:1971;35.
    • (1971) Trans. Amer. Math. Soc. , vol.158 , pp. 35
    • Conley, C.1    Easton, R.2
  • 44
    • 0007230746 scopus 로고
    • Factorization properties of birational mappings
    • Boukraa S., Maillard J-M. Factorization properties of birational mappings. Physica A. 220:1995;403.
    • (1995) Physica a , vol.220 , pp. 403
    • Boukraa, S.1    Maillard, J-M.2
  • 47
    • 0001001511 scopus 로고
    • Singularity, complexity, and quasi-integrability of rational mappings
    • Viallet C.M., Falqui G. Singularity, complexity, and quasi-integrability of rational mappings. Comm. Math. Phys. 154:1993;111.
    • (1993) Comm. Math. Phys. , vol.154 , pp. 111
    • Viallet, C.M.1    Falqui, G.2
  • 50
    • 0039506299 scopus 로고    scopus 로고
    • Göttingen
    • C.F. Gauss, Werke, Göttingen, pp. 1870-1927.
    • Gauss, C.F.1    Werke2
  • 51
    • 0000130651 scopus 로고
    • Die Theorie der algebraischen Zahlkörper
    • D. Hilbert, Die Theorie der algebraischen Zahlkörper, Jber. Deutsch. Math. Verein. 4 (1987) 175; Gesammelte Abhand-lungen, vol. I, Springer, Berlin, 1932, p. 63 (Chelsea 1967).
    • (1987) Jber. Deutsch. Math. Verein. , vol.4 , pp. 175
    • Hilbert, D.1
  • 52
    • 0040691496 scopus 로고
    • Springer, Berlin, Chelsea
    • D. Hilbert, Die Theorie der algebraischen Zahlkörper, Jber. Deutsch. Math. Verein. 4 (1987) 175; Gesammelte Abhand-lungen, vol. I, Springer, Berlin, 1932, p. 63 (Chelsea 1967).
    • (1932) Gesammelte Abhand-lungen , vol.1 , pp. 63


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