The existence of Zariski dense orbits for polynomial endomorphisms of the affine plane
2017 ◽
Vol 153
(8)
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pp. 1658-1672
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Keyword(s):
In this paper we prove the following theorem. Let $f$ be a dominant polynomial endomorphism of the affine plane defined over an algebraically closed field of characteristic $0$. If there is no nonconstant invariant rational function under $f$, then there exists a closed point in the plane whose orbit under $f$ is Zariski dense. This result gives us a positive answer to a conjecture proposed by Medvedev and Scanlon, by Amerik, Bogomolov and Rovinsky, and by Zhang for polynomial endomorphisms of the affine plane.
2019 ◽
Vol 156
(2)
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pp. 325-339
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Keyword(s):
2014 ◽
Vol 10
(08)
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pp. 2187-2204
2000 ◽
Vol 62
(3)
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pp. 493-509
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2015 ◽
Vol 159
(1)
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pp. 165-186
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Keyword(s):
Keyword(s):
Keyword(s):
1959 ◽
Vol 14
◽
pp. 223-234
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Keyword(s):
2013 ◽
Vol 89
(2)
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pp. 234-242
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2014 ◽
Vol 35
(7)
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pp. 2242-2268
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2011 ◽
Vol 11
(2)
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pp. 221-271
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