Related papers: Bifurcations of unimodal maps
Motivated by a recent series of diametrically opposed articles on the relative value of statistical methods for the analysis of path diagrams in the social sciences, we discuss from a primarily theoretical perspective selected fundamental…
Cartograms combine statistical and geographical information in thematic maps, where areas of geographical regions (e.g., countries, states) are scaled in proportion to some statistic (e.g., population, income). Cartograms make it possible…
In this paper we investigate the ability of some recently introduced discrete kinetic models of vehicular traffic to catch, in their large time behavior, typical features of theoretical fundamental diagrams. Specifically, we address the…
We show that the connectedness of the set of parameters for which the over-rotation interval of a bimodal interval map is constant. In other words, the over-rotation interval is a monotone function of a bimodal interval map.
We give a complete structural characterisation of the map the positive branch of a one-way pattern implements. We start with the representation of the positive branch in terms of the phase map decomposition, which is then further analysed…
Computational topology has recently known an important development toward data analysis, giving birth to the field of topological data analysis. Topological persistence, or persistent homology, appears as a fundamental tool in this field.…
We introduce a renormalization procedure which allows us to study in a unified and concise way different properties of the irrational rotations on the unit circle $\beta \mapsto \set{\alpha+\beta}$, $\alpha \in \R\setminus \Q$. In…
We formulate and prove $\textit{a priori}$ bounds for the renormalization of H\'enon-like maps (under certain regularity assumptions). This provides a certain uniform control on the small-scale geometry of the dynamics, and ensures…
Recent progress concerning regularization of supersymmetric theories is reviewed. Dimensional reduction is reformulated in a mathematically consistent way, and an elegant and general method is presented that allows to study the…
We apply the algebraic-geometric techniques developed for the study of mappings which have the singularity confinement property to mappings which are integrable through linearisation. The main difference with respect to the previous studies…
We study the expanding properties of random perturbations of regular interval maps satisfying the summability condition of exponent one. Under very general conditions on the interval maps and perturbation types, we prove strong stochastic…
Bifurcation phenomena are common in multi-dimensional multi-parameter dynamical systems. Normal form theory suggests that the bifurcations themselves are driven by relatively few parameters; however, these are often nonlinear combinations…
We define train track maps for graphs-of-groups $\cal G$ and exhibit the precise conditions under which the fundamental finiteness properties known for classical train track maps extend to this generalization. These finiteness properties…
Functional conjugation methods are used to analyze the global structure of various renormalization group trajectories, and to gain insight into the interplay between continuous and discrete rescaling. With minimal assumptions, the methods…
We study the behavior of solutions of mutually coupled equations in heterogeneous random graphs. Heterogeneity means that some equations receive many inputs whereas most of the equations are given only with a few connections. Starting from…
We study two-dimensional, two-piece, piecewise-linear maps having two saddle fixed points. Such maps reduce to a four-parameter family and are well known to have a chaotic attractor throughout open regions of parameter space. The purpose of…
In this paper we build a geometric model for the renormalisation of irrationally indifferent fixed points of holomorphic maps with two critical points. The model incorporates arithmetic properties of the rotation number at the fixed point,…
A new kind of diagrams is presented, showing the causal structure of bimetric interactions.
Numerical simulations of coupled map lattices (CMLs) and other complex model systems show an enormous phenomenological variety that is difficult to classify and understand. It is therefore desirable to establish analytical tools for…
Directed acyclic graphs are the basic representation of the structure underlying Bayesian networks, which represent multivariate probability distributions. In many practical applications, such as the reverse engineering of gene regulatory…