相关论文: Approximate Description of the Mandelbrot Set. The…

Using computer graphics and visualization algorithms, we extend in this work the results obtained analytically in [1], on the connectivity domains of alternated Julia sets, defined by switching the dynamics of two quadratic Julia sets. As…

We compare the results of renormalization-group and lattice studies for the properties of the electroweak phase transition. This comparison reveals the mechanisms that underlie the phenomenology of the phase transition.

In this paper we prove the following: Take any "small Mandelbrot set" and zoom in a neighborhood of a parabolic or Misiurewicz parameter in it, then we can see a quasiconformal image of a Cantor Julia set which is a perturbation of a…

These lecture notes have been written for a short introductory course on universality and renormalization group techniques given at the VIII Modave School in Mathematical Physics by the author, intended for PhD students and researchers new…

In frameworks of the phenomenological approach we analyze of the phase diagram of mixed compounds. We obtain space groups of symmetry of the real structures as result of phase transition from close-packed degenerate structure. The theory of…

We review and propose to use of associated dynamical system to explore the phase transition phenomena in $p$-adic statistical mechanics setting, by means of the renormalization techniques. Main focus of the paper is the $p$-adic…

Concerning renormalisation group theory applied to phase transitions, we examine the value of positive numerical and analytical evidence, the divergent short-wavelength behaviour of classical free fields and the absence of UV-divergences in…

Working within the polynomial quadratic family, we introduce a new point of view on bifurcations which naturally allows to see the seat of bifurcations as the projection of a Julia set of a complex dynamical system in dimension three. We…

To analyze phase transitions in a nonequilibrium system we study its grand canonical partition function as a function of complex fugacity. Real and positive roots of the partition function mark phase transitions. This behavior, first found…

In this Note, we present recent developments in the Renormalization Theory of quadratic polynomials and discuss their applications, with an emphasis on the MLC conjecture, the problem of local connectivity of the Mandelbrot set, and on its…

We present a simple proof of Tan's theorem on asymptotic similarity between the Mandelbrot set and Julia sets at Misiurewicz parameters. Then we give a new perspective on this phenomenon in terms of Zalcman functions, that is, entire…

This paper is a survey, with few proofs, of ideas and notions related to self-similarity of groups, semi-groups and their actions. It attempts to relate these concepts to more familiar ones, such as fractals, self-similar sets, and…

We will show the Mandelbrot set $M$ is locally conformally inhomogeneous: the only conformal map $f$ defined in an open set $U$ intersecting $\partial M$ and satisfying $f(U\cap\partial M)\subset \partial M$ is the identity map. The proof…

We apply the Yang-Lee theory of phase transitions to an urn model of separation of sand. The effective partition function of this nonequilibrium system can be expressed as a polynomial of the size-dependent effective fugacity $z$. Numerical…

Following the ideas of A.~Douady, we give an alternative proof of the authors' result: for any boundary point $c_0$ of the Mandelbrot set $M$, we can find small quasiconformal copies of $M$ in $M$ that are encaged in nested quasiconformal…

The investigation of the Hamiltonian dynamical counterpart of phase transitions, combined with the Riemannian geometrization of Hamiltonian dynamics, has led to a preliminary formulation of a differential-topological theory of phase…

We introduce an analog in the context of rational maps of the idea of hyperbolic Dehn surgery from the theory of Kleinian groups. A surgery sequence is a sequence of postcritically finite maps limiting (in a precise manner) to a…

In this present paper, it is proposed the renormalization techniques in the investigation of phase transition phenomena in $p$-adic statistical mechanics. We mainly study $p$-adic $\l$-model on the Cayley tree of order two. We consider…

We study the scaling and universal behavior of temperature-driven first-order phase transitions in scalar models. These transitions are found to exhibit rich phenomena, though they are controlled by a single complex-conjugate pair of the…

We study a phase transition in a non-equilibrium model first introduced in [5], using the Yang-Lee description of equilibrium phase transitions in terms of both canonical and grand canonical partition function zeros. The model consists of…