A pr 2 00 5 Approximate Description of the Mandelbrot Set . Thermodynamic Analogy

Extension of the Douady-Hubbard's Theorem on Connectedness of the Mandelbrot Set to Symmetric Polynimials

A pr 2 00 6 HOPF BIFURCATION WITHIN THERMODYNAMIC REPRESENTATION

On base of Hamiltonian formalism, we show that Hopf bifurcation arrives, in the course of the system evolution, at creation of revolving region of the phase plane being bounded by limit cycle. A revolving phase plane with a set of limit cycles is presented in analogy with revolving vessel containing superfluid He 4. Within such a representation, fast varying angle is shown to be reduced to phas...

ar X iv : m at h - ph / 0 51 10 74 v 1 2 5 N ov 2 00 5 1 / f Noise in Fractal Quaternionic Structures

We consider the logistic map over quaternions H ∼ R 4 and different 2D projections of Mandelbrot set in 4D quaternionic space. The approximations (for finite number of iterations) of these 2D projections are fractal circles. We show that a point process defined by radiuses Rj of those fractal circles exhibits pure 1/f noise.

Module approximate amenability of Banach algebras

In the present paper, the concepts of module (uniform) approximate amenability and contractibility of Banach algebras that are modules over another Banach algebra, are introduced. The general theory is developed and some hereditary properties are given. In analogy with the Banach algebraic approximate amenability, it is shown that module approximate amenability and contractibility are the same ...

ar X iv : m at h - ph / 0 51 10 74 v 2 1 D ec 2 00 5 1 / f Noise in Fractal Quaternionic Structures

We consider the logistic map over quaternions H ∼ R 4 and different 2D projections of Mandelbrot set in 4D quaternionic space. The approximations (for finite number of iterations) of these 2D projections are fractal circles. We show that a point process defined by radiuses Rj of those fractal circles exhibits pure 1/f noise.