Related papers: Dynamics of a two parameter family of plane birati…
Continuing work begun in a previous paper, we study the real dynamics of a family of plane birational maps. This time we consider a parameter range where the real and complex dynamics are different. We show in particular that for one…
We give a detailed description of the dynamics of a family of birational mappings of the plane. The organizing theme of our analysis is that this family is essentially conjugate to the golden mean subshift.
We consider the family of piecewise linear maps $F(x,y)=\left(|x| - y + a, x - |y| + b\right),$ where $(a,b)\in \R^2$. In previous work, we identified a novel phenomenon: certain maps of this class possess one-dimensional invariant sets,…
We consider a family of birational transformations of two variables, depending on one parameter, for which simple rational expressions with integer coefficients, for the exact expression of the dynamical zeta function, have been…
This continues the investigation of a combinatorial model for the variation of dynamics in the family of rational maps of degree two, by concentrating on those varieties in which one critical point is periodic. We prove some general results…
We introduce and study the notion of a directional complexity and entropy for maps of degree 1 on the circle. For piecewise affine Markov maps we use symbolic dynamics to relate this complexity to the symbolic complexity. We apply a…
We investigate the dynamics of maps of the real line whose behavior on an invariant interval is close to a rational rotation on the circle. We concentrate on a specific two-parameter family, describing the dynamics arising from models in…
Very little is currently known about the dynamics of non-polynomial entire maps in several complex variables. The family of transcendental H\'enon maps offers the potential of combining ideas from transcendental dynamics in one variable,…
It has been known for some time that the topological entropy is a nondecreasing function of the parameter in the real quadratic family, which corresponds to the intuitive idea that more nonlinearity induces more complex dynamical behavior.…
We compare real and complex dynamics for automorphisms of rational surfaces that are obtained by lifting \chg{some} quadratic birational maps of the plane. In particular, we show how to exploit the existence of an invariant cubic curve to…
Topological entropy is a measure of complex dynamics. In this regard, multimodal maps play an important role when it comes to study low-dimensional chaotic dynamics or explain some features of higher dimensional complex dynamics with…
Bifurcation theory is the usual analytic approach to study the parameter space of a dynamical system. Despite the great power of prediction of these techniques, fundamental limitations appear during the study of a given problem. Nonlinear…
We study the dynamics of a family of replicator maps, depending on two parameters. Such studies are motivated by the analysis of the dynamics of evolutionary games under selections. From the dynamics viewpoint, we prove the existence of…
This work dynamically classifies a 9-parametric family of birational maps f : C2 -> C2. From the sequence of the degrees dn of the iterates of f, we find the dynamical degree delta(f) of f. We identify when dn grows periodically, linearly,…
We study the iterative behavior of the family of 3-step linear fractional recurrences and the family of birational maps they define. We determine all the possible periodicities within this family or, equivalently, the birational maps of…
Two-dimensional mappings obtained by coupling two piecewise increasing expanding maps are considered. Their dynamics is described when the coupling parameter increases in the expanding domain. By introducing a coding and by analysing an…
We consider the set of all 2-step recurrences (difference equations) that are given by linear fractional maps. These give birational maps of the plane. We determine the degree growth of these birational maps. We find the all the maps in…
Dynamical systems, whether continuous or discrete, are used by physicists in order to study non-linear phenomena. In the case of discrete dynamical systems, one of the most used is the quadratic map depending on a parameter. However, some…
In this paper we consider maps on the plane which are similar to quadratic maps in that they are degree 2 branched covers of the plane. In fact, consider for $\alpha$ fixed, maps $f_c$ which have the following form (in polar coordinates):…
We study the dynamics of meromorphic maps for a compact Kaehler manifold X. More precisely, we give a simple criterion that allows us to produce a measure of maximal entropy. We can apply this result to bound the Lyapunov exponents. Then,…