Related papers: Period tripling and quintupling renormalizations b…
The level set of an elliptic function is a doubly periodic point set in C. To obtain a wider spectrum of point sets, we consider, more generally, a Riemann surface S immersed in C^2 and its sections (``cuts'') by C. We give S a…
In this paper, we show that each expanding Thurston map $f : S^2\rightarrow S^2$ has $1+ deg f$ fixed points, counted with appropriate weight, where $ deg f$ denotes the topological degree of the map $f$. We then prove the equidistribution…
Decay to asymptotic steady state in one-dimensional logistic-like mappings is characterized by considering a phenomenological description supported by numerical simulations and confirmed by a theoretical description. As the control…
In this paper we establish $C^2$ a-priori bounds for the scaling ratios of critical circle mappings in a form that gives also a compactness property for the renormalization operator.
As a first application of our renormalisation group approach to non-local matrix models [hep-th/0305066], we prove (super-)renormalisability of Euclidean two-dimensional noncommutative \phi^4-theory. It is widely believed that this model is…
We show that for a certain family of integrable reversible transformations, the curves of periodic points of a general transformation cross the level curves of its integrals. This leads to the divergence of the normal form for a general…
Based on our studies done on two-dimensional autonomous systems, forced non-autonomous systems and time-delayed systems, we propose a unified methodology - that uses renormalization group theory - for finding out existence of periodic…
We report a comprehensive numerical study of the renormalization group flow of marginal couplings in $(3+1)$-dimensional projectable Ho\v{r}ava gravity. First, we classify all fixed points of the flow and analyze their stability matrices.…
In this paper, we extend the concept of generalized entropy to uniform spaces, allowing computations beyond metrizable settings. We apply this to parabolic dynamics - systems with a unique fixed point uniformly attracting all compact…
We investigate the spatiotemporal dynamics of a network of coupled chaotic maps, with varying degrees of randomness in coupling connections. While strictly nearest neighbour coupling never allows spatiotemporal synchronization in our…
Manifold reconstruction has been extensively studied for the last decade or so, especially in two and three dimensions. Recently, significant improvements were made in higher dimensions, leading to new methods to reconstruct large classes…
We study circle maps with a flat interval where the critical exponents at the two boundary points of the flat spot might be different. The space of such systems is partitioned in two connected parts whose common boundary only depends on the…
We introduce fibrewise compactifications in both the setting of locally compact Hausdorff spaces and continuous maps, and the parallel setting of $C^*$-algebras and nondegenerate multiplier-valued $*$-homomorphisms. In both situations, we…
In this paper we propose an elementary topological approach which unifies and extends various different results concerning fixed points and periodic points for maps defined on sets homeomorphic to rectangles embedded in euclidean spaces. We…
In the symmetric and the asymmetric trapezoid maps, as a slope of the trapezoid is increased, the period doubling cascade occurs and the symbolic sequence of periodic points is the Metropolis-Stein-Stein sequence and the convergence of the…
Recently, it has been claimed that some complex networks are self-similar under a convenient renormalization procedure. We present a general method to study renormalization flows in graphs. We find that the behavior of some variables under…
Given a self-map of a compact metric space $X$, we study periodic points of the map induced on the hyperspace of closed subsets of $X$. We give some necessary conditions on admissible sets of periods for these maps. Seemingly unrelated to…
In this paper we continue the study of renormalized entanglement entropy introduced in [1]. In particular, we investigate its behavior near an IR fixed point using holographic duality. We develop techniques which, for any static holographic…
For a class of polynomial maps of one variable with a parabolic fixed points and degrees bigger than $21$, the parabolic renormalization is introduced based on Fatou coordinates and horn maps, and a type of maps which are invariant under…
We examine thermodynamic formalism for a class of renormalizable dynamical systems which in the symbolic space is generated by the Thue-Morse substitution, and in complex dynamics by the Feigenbaum-Coullet-Tresser map. The basic question…