Related papers: On the relationship between Lozi maps and max-type…
We focus on evolution equations on co-evolving, infinite, graphs and establish a rigorous link with a class of nonlinear continuity equations, whose vector fields depend on the graphs considered. More precisely, weak solutions of the…
Several coupled maps models are sketched and reviewed in this short communication. First, a discrete logistic type model that was proposed for the symbiotic interaction of two species. Second, a model of many of these symbiotic species…
We propose a model for co-evolving ecosystems that takes into account two levels of description of an organism, for instance genotype and phenotype. Performance at the macroscopic level forces mutations at the microscopic level. These, in…
This paper is about the study of F-transforms based on overlap and grouping maps, residual and co-residual implicator over complete lattice from both constructive and axiomatic approaches. Further, the duality, basic properties, and the…
Different types of transformations of a dynamical system, that are compatible with the Hamiltonian structure, are discussed making use of a geometric formalism. Firstly, the case of canonoid transformations is studied with great detail and…
We investigate the presence of localized solutions in models described by a single real scalar field with generalized dynamics. The study offers a method to solve very intricate nonlinear ordinary differential equations, and we illustrate…
A new ansatz is presented for a Lax pair describing systems of particles on the line interacting via (possibly nonsymmetric) pairwise forces. Particular cases of this yield the known Lax pairs for the Calogero-Moser and Toda systems, as…
This work surveys the topological and statistical properties of real quadratic maps and investigates the complex quadratic maps under holomorphic and non-holomorphic singular perturbations.
We study Zariski-like topologies on a proper class $X\varsubsetneqq L$ of a complete lattice $\mathcal{L}=(L,\wedge ,\vee ,0,1)$. We consider $X$ with the so called classical Zariski topology $(X,\tau ^{cl})$ and study its topological…
In this note we summarize the connections between equilibrium and slow out of equilibrium dynamics in finite dimensional glasses, such as we understand them today. If we assume that a finite-dimensional system is stable with respect to a…
We generalized several results for the arithmetic dynamics of monomial maps, including Silverman's conjectures on height growth, dynamical Mordell-Lang conjecture, and dynamical Manin-Mumford conjecture. These results are originally known…
In this work a theory is developed for unifying large classes of nonlinear discrete-time dynamical systems obeying a superposition of a weighted maximum or minimum type. The state vectors and input-output signals evolve on nonlinear spaces…
Family of replica matrices, related to general ultrametric spaces, is introduced. These matrices generalize the known Parisi matrices. Some functionals of replica approach are computed.
We study the measurable dynamics of transformations on profinite groups, in particular of those which factor through sufficiently many of the projection maps; these maps generalize the 1-Lipschitz maps on $\mathbb Z_p$.
In this paper it is shown that a generalized circulant matrix underlies every weakly Coupled Map Lattice (CML), independently of the form of the coupling term. Therefore, this matrix will appear always perturbative methods are used to get…
We extend some known results from smooth dynamical systems to the category of Lipschitz homeomorphisms of compact metric spaces. We consider dynamical properties as robust expansiveness and structural stability allowing Lipschitz…
Multilevel modeling extends traditional modeling techniques with a potentially unlimited number of abstraction levels. Multilevel models can be formally represented by multilevel typed graphs whose manipulation and transformation are…
For the family of Lozi maps $L_{a,b}$, we consider parameter pairs for which the f\mbox{}ixed point $X$ has no homoclinic points and the period-two orbit $\{P,P'\}$ is attracting. For such parameters, let $\ell$ be the set of accumulation…
We determine the conditions for the existence or not of cycles for several families of generalized 3x + 1 mappings and develop a method to find them.
There is a well-known correspondence between infinite trees and ultrametric spaces which can be interpreted as an equivalence of categories and comes from considering the end space of the tree. In this equivalence, uniformly continuous maps…