References
- G. S. Call and J. H. Silverman, Canonical heights on varieties with morphisms, Compositio Math. 89 (1993), no. 2, 163-205.
- L. Denis, Points periodiques des automorphismes affines, J. Reine Angew. Math. 467 (1995), 157-167.
-
T.-C. Dinh, Sur les endomorphismes polynomiaux permutables de
${\mathbb{C}}^2$ , Ann. Inst. Fourier (Grenoble) 51 (2001), no. 2, 431-459. https://doi.org/10.5802/aif.1828 -
T.-C. Dinh and N. Sibony, Sur les endomorphismes holomorphes permutables de
${\mathbb{P}}^k$ , Math. Ann. 324 (2002), no. 1, 33-70. https://doi.org/10.1007/s00208-002-0328-2 - N. Fakhruddin, Questions on self maps of algebraic varieties, J. Ramanujan Math. Soc. 18 (2003), no. 2, 109-122.
- J.-E. Fornaess and N. Sibony, Complex dynamics in higher dimension. I, Complex analytic methods in dynamical systems (Rio de Janeiro, 1992). Asterisque No. 222 (1994), 5, 201-231.
- S. Hartshorne, Algebraic Geometry, Graduate Texts in Mathematics, No. 52. SpringerVerlag, New York-Heidelberg, 1977.
- S. Kawaguchi, Local and global canonical height functions for affine space regular automorphisms, Algebra Number Theory 7 (2013), no. 5, 1225-1252. https://doi.org/10.2140/ant.2013.7.1225
- S. Kawaguchi and J. H. Silverman, Dynamics of projective morphisms having identical canonical heights, Proc. Lond. Math. Soc. (3) 95 (2007), no. 2, 519-544. https://doi.org/10.1112/plms/pdm022
-
C. Lee, An upper bound for the height for regular affine automorphisms on
${\mathbb{A}}^n$ , Math. Ann. 355 (2013), no. 1, 1-16. https://doi.org/10.1007/s00208-011-0775-8 - C. Lee, The maximal ratio of coefficients of divisors and the upper bound of height, preprint, ArXiv:1002.3357, 20.
- A. Levy, The space of morphisms on projective spaces, Acta Arith. 146 (2011), 13-31. https://doi.org/10.4064/aa146-1-2
- S. Marcello, Sur les propietes arithmetiques des iteres d'automorphismes reguliers, C. R. Acad. Sci. Paris Ser. I Math. 331 (2000), no. 1, 11-16. https://doi.org/10.1016/S0764-4442(00)00325-6
- A. Medvedev and T. Scanlon, Polynomial dynamics, preprint, arXiv:0901.2352, 2009.
- A. Moriwaki, Arithmetic height functions over finitely generated fields, Invent. Math. 140 (2000), no. 1, 101-142. https://doi.org/10.1007/s002220050358
- D. G. Northcott, Periodic points on an algebraic variety, Ann. of Math. (2) 51 (1950), 167-177. https://doi.org/10.2307/1969504
- J. F. Ritt, Permutable rational functions, Trans. Amer. Math. Soc. 25 (1923), no. 3, 399-488. https://doi.org/10.1090/S0002-9947-1923-1501252-3
-
N. Sibony, Dynamique des applications rationnelles de
${\mathbb{P}}^k$ , Dynamique et geometrie complexes (Lyon, 1997), ix-x, xi-xii, 97-185, Panor. Syntheses, 8, Soc. Math. France, Paris, 1999. - J. H. Silverman, The Arithmetic of Dynamical System, Graduate Texts in Mathematics, 241. Springer, New York, 2007.
- J. H. Silverman and M. Hindry, Diophantine Geometry, Graduate Texts in Mathematics, 201. Springer-Verlag, New York, 2000.
- X. Yuan, Big line bundles over arithmetic varieties, Invent. Math. 173 (2008), no. 3, 603-649. https://doi.org/10.1007/s00222-008-0127-9
- X. Yuan and S. Zhang, Calabi theorem and algebraic dynamics, preprint, 2009.