We propose to study dynamical systems in which the real line acts by automorphisms of operator algebras; the algebras will arise from some variant of the crossed-product construction, and the systems will exhibit behaviour reminiscent of physical systems. The main examples involve higher-rank graph algebras or semigroup crossed products of number-theoretic origin. We will analyse the ideal structure of the system, the KMS states of the system (the analogue of equilibrium states), and symmetries of the KMS states. We expect to make significant contributions to our understanding of dynamical phenomena arising in number theory, and we believe that our key examples will exhibit interesting new phenomena
We propose to study dynamical systems in which the real line acts by automorphisms of operator algebras; the algebras will arise from some variant of the crossed-product construction, and the systems will exhibit behaviour reminiscent of physical systems. The main examples involve higher-rank graph algebras or semigroup crossed products of number-theoretic origin. We will analyse the ideal structure of the system, the KMS states of the system (the analogue of equilibrium states), and symmetries of the KMS states. We expect to make significant contributions to our understanding of dynamical phenomena arising in number theory, and we believe that our key examples will exhibit interesting new phenomena
