Dynamical Scale Transform in Tropical Geometry

Tropical geometry works as a kind of dynamical scale transform. It connects real rational dynamics with piecewise linear dynamics, which are expressed through max and plus algebras. Tsuyoshi Kato uses this link to compare orbits in different rational dynamics by reducing them to the piecewise linear case.

The book presents several applications. These include a coarse sorting of partial differential equations according to the global behaviour of their solutions, another construction of infinite quasi-recursive rational dynamics from the automaton of the Burnside group, and a third examination of near-periodicity of the pentagram map acting on the moduli space of twisted polygons.

The text also relates a lamplighter group from the theory of automata groups to box and ball systems linked to the KdV equation. It is written to be self-contained, with accounts of automata groups, box and ball systems and the pentagram map included.

Researchers in dynamical systems, geometry and mathematical physics will find it useful.

Edition note: published by World Scientific Publishing Company. ISBN-13: 9789814635363.