Surjective endomorphisms of projective surfaces: the existence of infinitely many dense orbits
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Amerik, E.: Existence of non-preperiodic algebraic points for a rational self-map of infinite order. Math. Res. Lett. 18(02), 251–256 (2011)
Amerik, E., Campana, F.: Fibrations méromorphes sur certaines variétés à fibré canonique trivial. Pure Appl. Math. Q. 4(2), 509–546 (2008)
Bell, J. P., Ghioca, D., Tucker, T. J.: The dynamical Mordell–Lang conjecture, mathematical surveys and monographs. Am. Math. Soc. 210, 978-1-4704-2408-4 (2016)
Bell, J.P., Ghioca, D., Tucker, T.J.: Applications of $$p$$-adic analysis for bounding periods of subvarieties under étale maps, 2014, 1073–7928. Int. Math. Res. Not. IMRN 11, 3576–3597 (2015)
Boucksom, S., de Fernex, T., Favre, C.: The volume of an isolated singularity. Duke Math. J. 161(8), 1455–1520 (2012)
Broustet, A., Gongyo, Y.: Remarks on log Calabi-Yau structure of varieties admitting polarized endomorphisms. Taiwanese J. Math. 21(3), 569–582 (2017)
Broustet, A., Höring, A.: Singularities of varieties admitting an endomorphism. Math. Ann. 360(1–2), 439–456 (2014)
Cascini, P., Meng, S., Zhang, D.-Q.: Polarized endomorphisms of normal projective threefolds in arbitrary characteristic. Math. Ann. 378, 637–665 (2020)
Dinh, T.-C., Nguyên, V.-A., Truong, T.T.: Equidistribution for meromorphic maps with dominant topological degree. Indiana Univ. Math. J. 64(6), 1805–1828 (2015)
Fujino, O.: Fundamental theorems for the log minimal model program. Publ. Res. Inst. Math. Sci. 47(3), 727–789 (2011)
Fujino, O.: Minimal model theory for log surfaces in Fujiki’s class. Nagoya Math. J. 244, 256–282 (2021)
Ghioca, D., Satriano, M.: Density of orbits of dominant regular self-maps of semiabelian varieties. Trans. Am. Math. Soc. 371(9), 6341–6358 (2019)
Ghioca, D., Scanlon, T.: Density of orbits of endomorphisms of abelian varieties, 1088–6850. Trans. Am. Math. Soc. 369(1), 447–466 (2017)
Guedj, V.: Ergodic properties of rational mappings with large topological degree, 0003486X. Ann. Math. 161(3), 1589–1607 (2005)
Hartshorne, R.: Algebraic geometry, Grad. Texts in Math., Springer-Verlag, 52, 0-387-90244-9, (1977)
Iitaka, S.: Algebraic Geometry—An Introduction to Birational Geometry of Algebraic Varieties, Grad. Texts in Math., Springer-Verlag, 76, 0-387-90546-4, (1982)
Kollár, J., Mori, S.: Birational Geometry of Algebraic Varieties, Cambridge Tracts in Mathematics. Cambridge University Press (1998)
Matsuzawa, Y., Yoshikawa, S.: Kawaguchi-Silverman conjecture for endomorphisms on rationally connected varieties admitting an int-amplified endomorphism. Math. Ann. 382, 1681–1704 (2022)
Medvedev, A., Scanlon, T.: Invariant varieties for polynomial dynamical systems. Ann. Math. 179, 81–177 (2014)
Meng, S., Zhang, D.-Q.: Kawaguchi-Silverman conjecture for surjective endomorphisms, Documenta Mathematica (to appear), arXiv:1908.01605
Meng, S.: Building blocks of amplified endomorphisms of normal projective varieties. Math. Z. 294(3), 1727–1747 (2020)
Meng, S., Zhang, D.-Q.: Building blocks of polarized endomorphisms of normal projective varieties, 0001–8708. Adv. Math. 325, 243–273 (2018)
Milnor, J.: Dynamics in one complex variable. (AM-160): Third Edition, Princeton University Press, 9780691124889, (2006)
Nakayama, N.: A variant of Shokurov’s criterion of toric surface. Algebraic varieties and automorphism groups. Advanced Studies in Pure Mathematics, 75, Mathematical Society of Japan (2017)
Nakayama, N.: On normal Moishezon surfaces admitting non-isomorphic surjective endomorphisms, 1923, RIMS Preprints (2020)
Nakayama, N.: On the structure of normal projective surfaces admitting non-isomorphic surjective endomorphisms, 1934, RIMS Preprints (2020)
Nakayama, N.: Ruled surfaces with non-trivial surjective endomorphisms. Kyushu J. Math. 56(2), 433–446 (2002)
Wahl, J.: A characteristic number for links of surface singularities. J. Am. Math. Soc. 3(3), 625–637 (1990)
Xie, J.: The existence of Zariski dense orbits for endomorphisms of projective surfaces (with an appendix in collaboration with Thomas Tucker). J. Am. Math. Soc. (published online), arXiv:1905.07021
Xie, J.: The existence of Zariski dense orbits for polynomial endomorphisms of the affine plane. Compos. Math. 153(8), 1658–1672 (2017)
Zhang, D.-Q.: Polarized endomorphisms of uniruled varieties with an appendix by Y. Fujimoto and N. Nakayama. Compos. Math. 146(1), 145–168 (2010)