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In this paper, we study the relation between two dynamical systems $(V,f)$ and $(V,g)$ with $f\circ g = g \circ f$. As an application, we show that an endomorphism (respectively a polynomial map with Zariski dense, of bounded $\Pre(f)$) has only finitely many endomorphisms (respectively polynomial maps) of bounded degree which are commutable with $f$.
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참고문헌 (22)
참고문헌 신청
A. Levy / 2011 / The space of morphisms on projective spaces / Acta Arith 146 : 13 ~ 31
A. Medvedev / 2009 / Polynomial dynamics / arXiv:0901.2352
A. Moriwaki / 2000 / Arithmetic height functions over finitely generated fields / Invent. Math 140 (1) : 101 ~ 142
C. Lee / / The maximal ratio of coefficients of divisors and the upper bound of height / ArXiv:1002.3357, 20
C. Lee / 2013 / An upper bound for the height for regular affine automorphisms on An / Math. Ann 355 (1) : 1 ~ 16
A. Medvedev / 2009 / Polynomial dynamics / arXiv:0901.2352
A. Moriwaki / 2000 / Arithmetic height functions over finitely generated fields / Invent. Math 140 (1) : 101 ~ 142
C. Lee / / The maximal ratio of coefficients of divisors and the upper bound of height / ArXiv:1002.3357, 20
C. Lee / 2013 / An upper bound for the height for regular affine automorphisms on An / Math. Ann 355 (1) : 1 ~ 16
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