DEGENERATION OF ENDOMORPHISMS OF THE COMPLEX PROJECTIVE SPACE IN THE HYBRID SPACE
2018 ◽
Vol 19
(4)
◽
pp. 1141-1183
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Keyword(s):
Blow Up
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We consider a meromorphic family of endomorphisms of degree at least 2 of a complex projective space that is parameterized by the unit disk. We prove that the measure of maximal entropy of these endomorphisms converges to the equilibrium measure of the associated non-Archimedean dynamical system when the system degenerates. The convergence holds in the hybrid space constructed by Berkovich and further studied by Boucksom and Jonsson. We also infer from our analysis an estimate for the blow-up of the Lyapunov exponent near a pole in one-dimensional families of endomorphisms.
2001 ◽
Vol 73
(4)
◽
pp. 475-482
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Keyword(s):
2005 ◽
Vol 07
(05)
◽
pp. 583-596
◽
2020 ◽
Vol 17
(5)
◽
pp. 744-747
2002 ◽
Vol 66
(3)
◽
pp. 465-475
◽
1998 ◽
Vol 14
(1)
◽
pp. 1-8
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Keyword(s):