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EQUIDISTRIBUTION OF PERIODIC POINTS OF SOME AUTOMORPHISMS ON K3 SURFACES
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 Title & Authors
EQUIDISTRIBUTION OF PERIODIC POINTS OF SOME AUTOMORPHISMS ON K3 SURFACES
Lee, Chong-Gyu;
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 Abstract
We say (W, {}) is a polarizable dynamical system of several morphisms if are endomorphisms on a projective variety W such that is linearly equivalent to for some ample line bundle L on W and for some q > t. If q is a rational number, then we have the equidistribution of small points of given dynamical system because of Yuan`s work [13]. As its application, we can build a polarizable dynamical system of an automorphism and its inverse on a K3 surface and can show that its periodic points are equidistributed.
 Keywords
equidistribution;height;dynamical system;K3 surface;auto-morphism;
 Language
English
 Cited by
1.
HEIGHT ESTIMATES FOR DOMINANT ENDOMORPHISMS ON PROJECTIVE VARIETIES,;

East Asian mathematical journal, 2016. vol.32. 1, pp.61-75 crossref(new window)
1.
HEIGHT ESTIMATES FOR DOMINANT ENDOMORPHISMS ON PROJECTIVE VARIETIES, East Asian mathematical journal, 2016, 32, 1, 61  crossref(new windwow)
2.
The equidistribution of small points for strongly regular pairs of polynomial maps, Mathematische Zeitschrift, 2013, 275, 3-4, 1047  crossref(new windwow)
 References
1.
A. Baragar and D. McKinnon, K3 surfaces, rational curves, and rational points, J. Number Theory 130 (2010), no. 7, 1470-1479. crossref(new window)

2.
M. H. Baker and R. Rumely, Equidistribution of small points, rational dynamics, and potential theory, Ann. Inst. Fourier (Grenoble) 56 (2006), no. 3, 625-688. crossref(new window)

3.
Y. Bilu, Limit distribution of small points on algebraic tori, Duke Math. J. 89 (1997), no. 3, 465-476. crossref(new window)

4.
A. Chambert-Loir, Mesures et equidistribution sur les espaces de Berkovich, J. Reine Angew. Math. 595 (2006), 215-235.

5.
W. Fulton, Intersection Theory, Second edition, Springer-Verlag, Berlin, 1998.

6.
N. Fakhruddin, Questions on self maps of algebraic varieties, J. Ramanujan Math. Soc. 18 (2003), no. 2, 109-122.

7.
C. Favre and J. Rivera-Letelier, Equidistribution quantitative des points de petite hau- teur sur la droite projective, Math. Ann. 335 (2006), no. 2, 311-361. crossref(new window)

8.
S. Kawaguchi, Canonical heights, invariant currents, and dynamical eigensystems of morphisms for line bundles, J. Reine Angew. Math. 597 (2006), 135-173.

9.
J. H. Silverman, The Arithmetic of Dynamical System, Springer, 2007.

10.
J. H. Silverman, Rational points on K3 surfaces: a new canonical height, Invent. Math. 105 (1991), no. 2, 347-373. crossref(new window)

11.
J. H. Silverman and M. Hindry, Diophantine Geometry: An introduction, Springer, 2000.

12.
L. Szpiro, E. Ullmo, and S. Zhang, Equirepartition des petits points, Invent. Math. 127 (1997), no. 2, 337-347. crossref(new window)

13.
X. Yuan, Big line bundles over arithmetic varieties, Invent. Math. 173 (2008), no. 3, 603-649. crossref(new window)

14.
S. Zhang, Small points and adelic metrics J. Algebraic Geom. 4 (1995), no. 2, 281-300.