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Factorization properties of birational mappings

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  • Boukraa, S
  • Maillard, J-M

Abstract

We analyse birational mappings generated by transformations on q × q matrices which correspond respectively to two kinds of transformations: the matrix inversion and a permutation of the entries of the q × q matrix. Remarkable factorization properties emerge for quite general involutive permutations.

Suggested Citation

  • Boukraa, S & Maillard, J-M, 1995. "Factorization properties of birational mappings," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 220(3), pages 403-470.
    • Handle: RePEc:eee:phsmap:v:220:y:1995:i:3:p:403-470
    DOI: 10.1016/0378-4371(95)00220-2
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    References listed on IDEAS

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    1. Boukraa, S. & Maillard, J-M. & Rollet, G., 1994. "Integrable mappings and polynomial growth," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 209(1), pages 162-222.
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    Cited by:

    1. Abarenkova, N. & Anglès d'Auriac, J.-C. & Maillard, J.-M., 1997. "More integrable birational mappings," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 237(1), pages 123-134.
    2. Abarenkova, N. & Anglès d'Auriac, J.-Ch. & Boukraa, S. & Hassani, S. & Maillard, J.-M., 2000. "Real Arnold complexity versus real topological entropy for a one-parameter-dependent two-dimensional birational transformation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 281(1), pages 151-172.
    3. Boukraa, S. & Hassani, S. & Maillard, J.-M., 1997. "New integrable cases of a Cremona transformation: a finite-order orbits analysis," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 240(3), pages 586-621.
    4. Abarenkova, N. & Anglès d'Auriac, J.-Ch. & Boukraa, S. & Hassani, S. & Maillard, J.-M., 1999. "Rational dynamical zeta functions for birational transformations," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 264(1), pages 264-293.

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    1. Abarenkova, N. & Anglès d'Auriac, J.-Ch. & Boukraa, S. & Hassani, S. & Maillard, J.-M., 2000. "Real Arnold complexity versus real topological entropy for a one-parameter-dependent two-dimensional birational transformation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 281(1), pages 151-172.
    2. Boukraa, S. & Hassani, S. & Maillard, J.-M., 1997. "New integrable cases of a Cremona transformation: a finite-order orbits analysis," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 240(3), pages 586-621.
    3. Abarenkova, N. & Anglès d'Auriac, J.-C. & Maillard, J.-M., 1997. "More integrable birational mappings," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 237(1), pages 123-134.
    4. Abarenkova, N. & Anglès d'Auriac, J.-Ch. & Boukraa, S. & Hassani, S. & Maillard, J.-M., 1999. "Rational dynamical zeta functions for birational transformations," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 264(1), pages 264-293.

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