Dynamics of Rational Surface Automorphisms: Linear Fractional Recurrences

Eric Bedford1, Kyoung-Hee Kim2
1Indiana University Bloomington, USA
2Florida State University, Tallahassee, USA

Tóm tắt

Từ khóa


Tài liệu tham khảo

Baker, A.: The theory of linear forms in logarithms. In: Baker, A., Masser, D.W. (eds.) Transcendence Theory: Advances and Applications, pp. 1–27. Academic Press, San Diego (1977)

Bedford, E., Diller, J.: Real and complex dynamics of a family of birational maps of the plane: the golden mean subshift. Am. J. Math. 127(3), 595–646 (2005)

Bedford, E., Diller, J.: Dynamics of a two parameter family of plane birational maps: maximal entropy. J. Geom. Anal. 16(3), 409–430 (2006)

Bedford, E., Kim, K.H.: Periodicities in linear fractional recurrences: degree growth of birational surface maps. Mich. Math. J. 54, 647–670 (2006)

Bedford, E., Lyubich, M., Smillie, J.: Polynomial diffeomorphisms of C 2. IV. The measure of maximal entropy and laminar currents. Invent. Math. 112(1), 77–125 (1993)

Bedford, E., Smillie, J.: Polynomial diffeomorphisms of C 2. II. Stable manifolds and recurrence. J. Am. Math. Soc. 4(4), 657–679 (1991)

Bedford, E., Smillie, J.: Real polynomial diffeomorphisms with maximal entropy: Tangencies. Ann. Math. (2) 160(1), 1–26 (2004)

Beukers, F., Cushman, R.: Zeeman’s monotonicity conjecture. J. Differ. Equ. 143, 191–200 (1998)

Cantat, S.: Dynamique des automorphismes des surfaces projectives complexes. C. R. Acad. Sci. Paris Sér. I Math. 328(10), 901–906 (1999)

Cantat, S.: Dynamique des automorphismes des surfaces K3. Acta Math. 187(1), 1–57 (2001)

Diller, J., Jackson, D., Sommese, A.: Invariant curves for birational surface maps. Trans. AMS 359, 2973–2991 (2007). math.AG/0505014

Floyd, W.: Growth of planar Coxeter groups, P.V. numbers, and Salem numbers. Math. Ann. 293, 475–483 (1992)

Fornæss, J.-E., Sibony, N.: Classification of recurrent domains for some holomorphic maps. Math. Ann. 301(4), 813–820 (1995)

Gromov, M.: Entropy, homology and semialgebraic geometry. In: Séminaire Bourbaki, vol. 1985/86. Astérisque No. 145–146, 5, pp. 225–240 (1987)

Harbourne, B.: Rational surfaces with infinite automorphism group and no antipluricanonical curve. Proc. AMS 99, 409–414 (1987)

Kocic, V.I., Ladas, G., Rodrigues, I.W.: On rational recursive sequences. J. Math. Anal. Appl. 173, 127–157 (1993)

Kulenovic, M., Ladas, G.: Dynamics of Second Order Rational Difference Equations. CRC Press, Boca Raton (2002)

Lyness, R.C.: Notes 1581, 1847, and 2952. Math. Gaz. 26, 62 (1942), 29, 231 (1945), and 45, 201 (1961)

McMullen, C.: Dynamics on K3 surfaces: Salem numbers and Siegel disks. J. Reine Angew. Math. 545, 201–233 (2002)

McMullen, C.: Dynamics on blowups of the projective plane. Publ. Sci. IHES 105, 49–89 (2007)

Pöschel, J.: On invariant manifolds of complex analytic mappings near fixed points. Exp. Math. 4(2), 97–109 (1986)

Ueda, T.: Critical orbits of holomorphic maps on projective spaces. J. Geom. Anal. 8, 319–334 (1998)

Washington, L.: Introduction to Cyclotomic Fields. Springer, Berlin (1997)

Yomdin, Y.: Volume growth and entropy. Isr. J. Math. 57(3), 285–300 (1987)

Zeeman, C.: Geometric unfolding of a difference equation. Lecture

Zehnder, E.: A simple proof of a generalization of a theorem by C.L. Siegel. In: Geometry and topology. Proc. III Latin Amer. School of Math., Inst. Mat. Pura Aplicada CNPq, Rio de Janeiro, 1976. Lecture Notes in Math., vol. 597, pp. 855–866. Springer, Berlin (1977)

Zhang, D.-Q.: Automorphism groups and anti-canonical curves. Math. Res. Lett. 15, 163–183 (2008)