It is proved that any SOо(1, d)-valued cocycle over an ergodic (probability) measurepreserving automorphism is cohomologous to a cocycle having one of three special forms; the recurrence property of such cocycles is also studied.
We provide a definition of a two-colored graph of a Morse-Smale diffeomorphism without heteroclinical intersection defined on the sphere $S^n$, $n\geq 4$ and prove that this graph is the complete topological invariant for such diffeomorphisms.
In a neighborhood of a singular point, we consider autonomous systems of ordinary differential equations for which one eigenvalue of the matrix of the linear part is zero and the remaining eigenvalues do not belong to the imaginary axis. We prove that the problem of finitely smooth equivalence can be solved for such systems by using finite segments of the Taylor series of their right-hand sides.
In a neighborhood of a singular point, we consider autonomous systems of ordinary differential equations such that the matrix of the linearized system has two pure imaginary eigenvalues, all other eigenvalues lying outside the imaginary axis. The problem of local finitely smooth equivalence of such systems is studied.
In this paper, we construct a new distribution corresponding to a real noble gas as well as the equation of state for it.