참고문헌
- N. Abarenkova, J.-Ch. Angles d'Auriac, S. Boukraa, S. Hassani and J.-M. Mail-lard, Real Arnold complexity versus real topological entropy for birational trans-formations, J. Phys. A: Math. Gen. 33 (2000), 1465-1501. https://doi.org/10.1088/0305-4470/33/8/301
- N. Abarenkova, J.-Ch. Angles d'Auriac, S. Boukraa and J.-M. Maillard, Growth complexity spectrum of some discrete dynamical systems, Physica D 130 (1999), 27-42. https://doi.org/10.1016/S0167-2789(99)00014-7
- N. Abarenkova, J.-Ch. Angles d'Auriac, S. Boukraa and J.-M. Maillard, Real topological entropy versus metric entropy for birational measure-preserving transformations, Physica D 144 (2000), 387-433. https://doi.org/10.1016/S0167-2789(00)00079-8
- E. Bedford and J. Diller, Energy and invariant measure for birational surface maps, preprint.
- E. Bedford and J. Diller, Real and complex dynamics of a family of birational maps of the plane: The golden mean subshift, preprint.
- E. Bedford and J. Diller, in preparation
-
E. Bedford and J. Smillie, Polynomial diffeomorphisms of
$C^2$ . VIII: Quasi-expansion, Amer. J. Math. 124 (2002), 221–271. https://doi.org/10.1353/ajm.2002.0008 - E. Bedford and J. Smillie, Real polynomial diffeomorphisms with maximal entropy: Tangencies, Math. DS/0103038.
- R. Devaney and Z. Nitecki, Shift automorphisms in the H´enon family, Comm. Math. Phys. 67 (1979), 48–137. https://doi.org/10.1007/BF01221362
-
J. Diller, Dynamics of birational maps of
$P^2$ , Indiana U. Math. J. 45 (1996), 721–772. - J. Diller and C. Favre, Dynamics of bimeromorphic maps of surfaces, Amer. J. of Math. 123 (2001), 1135–1169. https://doi.org/10.1353/ajm.2001.0038
-
C. Favre, Points périodiques d'applications birationnelles de
$P^2$ , Ann. Inst. Fourier (Grenoble) 48 (1998), 999–1023. - S. Friedland, Entropy of rational self-maps of projective varieties, in Dynamical Systems and Related Topics (Nagoya, 1990), pages 128–140. World Sci. Publishing, River Edge, NJ, 1991.
- J. Hietarinta and C. M. Viallet, Singularity confinement and chaos in discrete systems, Phys. Rev. Lett. 81 (1997), 325–328. https://doi.org/10.1103/PhysRevLett.81.325
- S. Morosawa, Y. Nishimura, M. Taniguchi and T. Ueda, Holomorphic Dynamics, Cambridge Univ. Press, 2000
- R. Oberste-Vorth, Complex horseshoes and the dynamics of mappings of two complex variables, Ph.D dissertation, Cornell Univ., Ithaca, NY, 1987
- T. Takenawa, A geometric approach to singularity confinement and algebraic entropy, J. Phys. A: Math. Gen. 34 (2001), L95–L102. https://doi.org/10.1088/0305-4470/34/10/103
- T. Takenawa, Algebraic entropy and the space of initial values for discrete dynamical systems, J. Phys. A: Math. Gen. 34 (2001), 10533–10545. https://doi.org/10.1088/0305-4470/34/48/317
- T. Takenawa, Discrete dynamical systems associated with root systems of indefinite type, Comm. Math. Phys. 224 (2001), 657–681. https://doi.org/10.1007/s002200100568
피인용 문헌
- On the degree growth of birational mappings in higher dimension vol.14, pp.4, 2004, https://doi.org/10.1007/BF02922170
- On the complex dynamics of birational surface maps defined over number fields vol.0, pp.0, 2016, https://doi.org/10.1515/crelle-2015-0113