Related papers: Renormalization in Lorenz maps -- completely invar…
A (discrete) dynamical system may have various symmetries and reversing symmetries, which together form its so-called reversing symmetry group. We study the set of 3D trace maps (obtained from two-letter substitution rules) which preserve…
By studying periodic points for rational maps on $\bm{C}^d$ with $p$ invariants, we show that they form an invariant variety of dimension $p$ if the periodicity conditions are `fully correlated', and a set of isolated points if the…
Proceeding by way of examples, we update the combinatorics of the treatment of Feynman diagrams with subdivergences in differential renormalization from more recent viewpoints in Epstein--Glaser renormalization in $x$-space.
Lorentz transformations of spin density matrices for a particle with positive mass and spin 1/2 are described by maps of the kind used in open quantum dynamics. They show how the Lorentz transformations of the spin depend on the momentum.…
We provide new examples of integrable rational maps in four dimensions with two rational invariants, which have unexpected geometric properties, as for example orbits confined to non algebraic varieties, and fall outside classes studied by…
It is known that the famous Feigenbaum-Coullet-Tresser period doubling universality has a counterpart for area-preserving maps of ${\fR}^2$. A renormalization approach has been used in \cite{EKW1} and \cite{EKW2} in a computer-assisted…
We study renormalizations of piecewise smooth homeomorphisms on the circle, by considering such maps as generalized interval exchange maps of genus one. Suppose that $Df$ is absolutely continuous on each interval of continuity and…
We investigate the structure of the centralizer and the normalizer of a local analytic or formal differential system at a nondegenerate stationary point, using the theory of Poincar\'e-Dulac normal forms. Our main results are concerned with…
Bifurcations of periodic orbits as an external parameter is varied are a characteristic feature of generic Hamiltonian systems. Meyer's classification of normal forms provides a powerful tool to understand the structure of phase space…
A long-standing question is what invariant sets can be shared by two maps acting on the same space. A similar question stands for invariant measures. A particular interesting case are expanding Markov maps of the circle. If the two involved…
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…
The search of high-order periodic orbits has been typically restricted to problems with symmetries that help to reduce the dimension of the search space. Well-known examples include reversible maps with symmetry lines. The present work…
Complex networks have acquired a great popularity in recent years, since the graph representation of many natural, social and technological systems is often very helpful to characterize and model their phenomenology. Additionally, the…
We propose a multivariate extension of the Lorenz curve based on multivariate rearrangements of optimal transport theory. We define a vector Lorenz map as the integral of the vector quantile map associated with a multivariate resource…
This work is concerned with planar real analytic differential systems with an analytic inverse integrating factor defined in a neighborhood of a regular orbit. We show that the inverse integrating factor defines an ordinary differential…
In this article we classify normal forms and unfoldings of linear maps in eigenspaces of (anti)-automorphisms of order two. Our main motivation is provided by applications to linear systems of ordinary differential equations, general and…
This work is dedicated to the study of both large-$N$ and perturbative quantum behaviors of Lifshitz nonlinear sigma models with dynamical critical exponent $z=2$ in 2+1 dimensions. We discuss renormalization and renormalization group…
Recurrence in the phase space of complex systems is a well-studied phenomenon, which has provided deep insights into the nonlinear dynamics of such systems. For dissipative systems, characteristics based on recurrence plots have recently…
A new generalized matrix inverse is derived which is consistent with respect to arbitrary nonsingular diagonal transformations, e.g., it preserves units associated with variables under state space transformations, thus providing a general…
Graph invariants provide a powerful analytical tool for investigation of abstract structures of graphs. They, combined in convenient relations, carry global and general information about a graph and its various substructures such as cycle…