Related papers: Bifurcations of unimodal maps

We apply renormalized entropy as a complexity measure to the logistic and sine-circle maps. In the case of logistic map, renormalized entropy decreases (increases) until the accumulation point (after the accumulation point up to the most…

A non-autonomous version of the standard map with a periodic variation of the parameter is introduced and studied. Symmetry properties in the variables and parameters of the map are found and used to find relations between rotation numbers…

Many real-world problems encountered in several disciplines deal with the modeling of time-series containing different underlying dynamical regimes, for which probabilistic approaches are very often employed. In this paper we describe…

We study dynamics and bifurcations of two-dimensional reversible maps having non-transversal heteroclinic cycles containing symmetric saddle periodic points. We consider one-parameter families of reversible maps unfolding generally the…

We study the effect of external forcing on the saddle-node bifurcation pattern of interval maps. By replacing fixed points of unperturbed maps by invariant graphs, we obtain direct analogues to the classical result both for random forcing…

Predicting extreme events in nonlinear dynamical systems is challenging due to a limited understanding of their statistical properties. This study numerically and theoretically investigates the statistical properties of infinite-modal maps…

We introduce orbital graphs and discuss some of their basic properties. Then we focus on their usefulness for search algorithms for permutation groups, including finding the intersection of groups and the stabilizer of sets in a group.

In four-dimensional symplectic maps complex instability of periodic orbits is possible, which cannot occur in the two-dimensional case. We investigate the transition from stable to complex unstable dynamics of a fixed point under parameter…

A physical measure on the attractor of a system describes the statistical behavior of typical orbits. An example occurs in unimodal dynamics. Namely, all infinitely renormalizable unimodal maps have a physical measure. For Lorenz dynamics,…

Random diffeomorphisms with bounded absolutely continuous noise are known to possess a finite number of stationary measures. We discuss dependence of stationary measures on an auxiliary parameter, thus describing bifurcations of families of…

In this paper we are concerned with quasi-periodic forced one dimensional maps. We consider a two parametric family of quasi-periodically forced maps such that the one dimensional map (before forcing) is unimodal and it has a full cascade…

This article is meant as a mathematical appendix or comment on [BT]. We first consider the notion of transcritical bifurcations of fixed points of general area-preserving maps, and then adress some questions related to [BT] on bifurcation…

In this paper we introduce the notion of cofrontal mappings, as the dual objects to frontal mappings, and study their basic local and global properties. Cofrontals are very special mappings and far from generic nor stable except for the…

We discuss recent results on decay of correlations for non-uniformly expanding maps. Throughout the discussion, we address the question of why different dynamical systems have different rates of decay of correlations and how this may…

In the present paper, we study harmonic mappings of complete Riemannian manifolds, as well as minimal and stable minimal submanifolds of complete Riemannian manifolds. We examine classical theorems in the theory of these manifolds from the…

We demonstrate the surprising strength of unimodal baselines in multimodal domains, and make concrete recommendations for best practices in future research. Where existing work often compares against random or majority class baselines, we…

This introduction surveys a renormalisation group perspective on log-Sobolev inequalities and related properties of stochastic dynamics. We also explain the relationship of this approach to related recent and less recent developments such…

Harmonic morphisms are maps between Riemannian manifolds that pull back harmonic functions to harmonic functions. These maps are characterized as horizontally weakly conformal harmonic maps and they have many interesting links and…

Concave in measure and d-concave in measure nonautonomous scalar ordinary differential equations given by coercive and time-compactible maps have similar properties to equations satisfying considerably more restrictive hypotheses. This…

Mainstream statistical methodology is generally applicable to data observed in Euclidean space. There are, however, numerous contexts of considerable scientific interest in which the natural supports for the data under consideration are…