Related papers: Variational structures for infinite transition orb…

We introduce the notion of Riemannian twistorial structure and we show that it provides new natural constructions of harmonic maps.

We construct Arnol'd cat map lattice field theories in phase space and configuration space. In phase space we impose that the evolution operator of the linearly coupled maps be an element of the symplectic group, in direct generalization of…

We study Markov multi-maps of the interval from the point of view of topological dynamics. Specifically, we investigate whether they have various properties, including topological transitivity, topological mixing, dense periodic points, and…

The regularity of monotone transport maps plays an important role in several applications to PDE and geometry. Unfortunately, the classical statements on this subject are restricted to the case when the measures are compactly supported. In…

In this paper we present methods for the synthesis of polynomial invariants for probabilistic transition systems. Our approach is based on martingale theory. We construct invariants in the form of polynomials over program variables, which…

In this work we consider variational properties of exact symplectic twist maps $T$ that act on the cotangent bundle of a torus, or on a ball bundle over a sphere. An example of such a map is the well-known Birkhoff billiard map…

For spatiotemporal chaos described by partial differential equations, there are generally locations where the dynamical variable achieves its local extremum or where the time partial derivative of the variable vanishes instantaneously. To a…

We provide a naturally isomorphic description of the persistence map from merge trees to barcodes in terms of a monotone map from the partition lattice to the subset lattice. Our description is local, which offers the potential to speed up…

There exists a variety of physically interesting situations described by continuous maps that are nondifferentiable on some surface in phase space. Such systems exhibit novel types of bifurcations in which multiple coexisting attractors can…

For area-preserving H\'enon-like maps and their compositions, we consider smooth perturbations that keep the reversibility of the initial maps but destroy their conservativity. For constructing such perturbations, we use two methods, the…

We examine shifted symplectic and Poisson structures on spaces of framed maps. We prove some results about shifted Poisson structures analogous to those in existing ones about symplectic structures. Then, we consider the space Map(X,D,Y) of…

Contrary to the established view of the Lorenz system as an archetype of dissipative chaos lacking conserved quantities, this work rigorously demonstrates the existence of a novel class of history-dependent dynamical invariants. Through a…

In this paper we study dynamical properties of the area preserving Henon map, as a discrete version of open Hamiltonian systems, that can exhibit chaotic scattering. Exploiting its geometric properties we locate the exit and entry sets,…

We study the transport properties of nonautonomous chaotic dynamical systems over a finite time duration. We are particularly interested in those regions that remain coherent and relatively non-dispersive over finite periods of time,…

Periodic orbits and cycles, respectively, play a significant role in discrete- and continuous-time dynamical systems (i.e. maps and flows). To succinctly describe their shifts when the system is applied perturbation, the notions of…

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…

Poincar\'e recognized that phase portraits are mainly structured around fixed points. Nevertheless, the knowledge of fixed points and their properties is not sufficient to determine the whole structure of chaotic attractors. In order to…

Invariant tori play a fundamental role in the dynamics of symplectic and volume-preserving maps. Codimension-one tori are particularly important as they form barriers to transport. Such tori foliate the phase space of integrable,…

We consider how the reduced dynamics of an open quantum system coupled to an environment admits the Poincar\'e symmetry. The reduced dynamics is described by a dynamical map, which is given by tracing out the environment from the total…

This note presents an approach to studying the iterates of a mapping whose restriction to the complement of a finite set is continuous and open. The main examples to which the approach can be applied are piecewise monotone mappings defined…