13 research outputs found
Ergodicity properties of -adic -rational dynamical systems with unique fixed point
We consider a family of -rational functions given on the set of
-adic field . Each such function has a unique fixed point. We study
ergodicity properties of the dynamical systems generated by -rational
functions. For each such function we describe all possible invariant spheres.
We characterize ergodicity of each -adic dynamical system with respect to
Haar measure reduced on each invariant sphere. In particular, we found an
invariant spheres on which the dynamical system is ergodic and on all other
invariant spheres the dynamical systems are not ergodic
Uniqueness of Gibbs Measure for Models With Uncountable Set of Spin Values on a Cayley Tree
We consider models with nearest-neighbor interactions and with the set
of spin values, on a Cayley tree of order .
It is known that the "splitting Gibbs measures" of the model can be described
by solutions of a nonlinear integral equation. For arbitrary we find
a sufficient condition under which the integral equation has unique solution,
hence under the condition the corresponding model has unique splitting Gibbs
measure.Comment: 13 page
Stability and monotonicity of Lotka–Volterra type operators
In the present paper,we investigate stability of trajectories ofLotka–Volterra (LV) type operators defined in finite dimensional simplex.We prove that any LV type
operator is a surjection of the simplex. It is introduced a newclass of LV-type operators, called MLV type ones, and we show that trajectories of the introduced operators converge. Moreover, we show that such kind of operators have totally different behavior than f-monotone LV type operators