The proposed research is an investigation of intermediate chaos in ergodic theory
of dynamical systems.
Among the topics are the ergodic theory
of hyperbolic groups, harmonic maps and integrable systems, left-orderability and exceptional Dehn surgery on two-bridge knots, the commensurability of knots and L2-unvariants, the number of hyperbolic 3-manifolds of a given volume, and 3-manifolds with Heegaard splittings of distance two.
He is a mathematician, specialising in ergodic theory
The presence of natural invariant measures allows one to study CA as measure-preserving dynamical systems, applying results from ergodic theory
Looking at recent results in the area of ergodic theory
(the mathematical study of dynamical systems with an invariant measure) concerning the complexity of the problem of classification of ergodic measure preserving transformations up to conjugacy, the structure of the outer automorphism group of a countable measure preserving equivalence relation, ergodic theoretic characterizations with the Haagerup approximation property, and cocycle superrigidity, the author of this monograph realized that these apparently diverse results can all be understood within a unified framework.
His research interests include nonlinear science and complexity, including quantum and classical statistical mechanics, neurodynamics, ergodic theory
and cellular automata.
Quasistrumian Shifts, Ergodic Theory
and Dynamical Systems forthcoming = math.
Thus, we can say that our approach to the dynamics of the vector field is based on maximisation of the mass carried by the flow [6, 7], which is not exactly what is typically used in the ergodic theory
Other applications of almost periodic functions are, for example, in Statistics, Number Theory, the Theory of Spectrum of Bounded Functions, the Theory of Semigroups of Bounded Linear Operators, Dynamical Systems and Ergodic Theory
BOWEN, Equilibrium States and the Ergodic Theory
of Anosov Diffeomorphisms, Lecture Notes in Mathematics, 470, Springer-Verlag, Berlinr, 1975.