Abstract:
We define families of Kuramoto models related to bounded symmetric domains. The families include Lohe unitary and spherical models as special cases. Our approach is
based on the construction proposed by Watanabe and Strogats. We replace the Poincare
disc and its $S^1$ boundary with bounded symmetric domains and with its
Bergman–Shilov boundaries. In Cartan's classifications there are four classical
domains of types I–IV. Here we consider the domains of types I, II, and III. For a fixed domain, there is a decreasing chain of components of
Bergman–Shilov boundaries. This leads to the families of Kuramoto models that we
describe here.
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