Solvability of nonlinear algebraic and integral equations in the theory of Gibbs measures (Ph.D. dissertation)

The dissertation is devoted to study splitting Gibbs measures for models with continuum set of spin values on a Cayley tree. In the first chapter of the dissertation is given main definitions and concepts of Gibbs measure on a Cayley tree. The second chapter is devoted to study the existence and uniqueness of periodic Gibbs measures for models with continuum set of spin values. In the third chapter it is constructed some models which has at least two periodic Gibbs measures.