3-14-1 Kouhoku-ku, Hiyoshi, Yokohama 223-8522, JAPAN
Speaker: Reimi Irokawa
Date and Time: 25th April 2019, 13:00 - 14:00 + 30min.
Place: Building 14, Room 631A/B
Title: Activity measures of dynamical systems over non-archimedean fields
A non-Archimedean field (NA field) is a field with an absolute value which satisfies the strong triangle inequality. For a polynomial with coefficients in an NA field K, one can consider a discrete dynamical system over K by iteration. Also, for an analytic family of polynomials, one can consider a deformation of dynamics. These dynamics appear naturally when one considers number-theoretic problems in complex & arithmetic dynamics. For an analytic family of polynomials over K, I constructed a measure, called an activity measure, which describes the stability of asymptotic of a critical point. Starting with gentle introduction on NA fields, I would explain stabilities related to families of dynamics over NA fields, construction of our measure, and their relations and properties.
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