Hyperbolic maps in p-adic dynamics

By Robert L. Benedetto. Ergodic Theory and Dynamical Systems, 2001

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p-Adic Dynamics and Sullivan's No Wandering Domains Theorem (2000, background): “In [ 3 ], a weaker version of Theorem 1.2 was proven using mapping properties of p-adic power series away from critical points.”
Canonical heights, transfinite diameters, and polynomial dynamics (2003, background): “More generally, it seems useful to try to put the p-adic theory of polynomial iteration on an equal footing with the complex theory [5, 6, 19, 20, 22].”
ON MINIMAL DECOMPOSITION OF p-ADIC POLYNOMIAL DYNAMICAL SYSTEMS (2010, background): “Recently the theory of Non-Archimedean, in particular of p-adic, dynamical systems has been intensively developed ([6, 7, 8], [13], [14], [16], [17], [18], [19, 20], [24], [26], [30], [33], [37], [39]).”
Components and Periodic Points in Non‐Archimedean Dynamics (2002, methodology): “It is also natural to ask about the relationship, similarities, and differences between non-archimedean dynamics and the archimedean theory of complex dynamics [2, 3, 4, 13, 15, 21].”