Related papers: An analysis of indeterminate points in discrete in…
We give general sufficient conditions to prove the convergence of marked point processes that keep record of the occurrence of rare events and of their impact for non-autonomous dynamical systems. We apply the results to sequential…
Intermittent dynamics is characterized by long periods of different types of dynamical characteristics, for instance almost periodic dynamics alternated by chaotic dynamics. Critical intermittency is intermittent dynamics that can occur in…
We introduce one dimensional sets to help describe and constrain the integral curves of an $n$ dimensional dynamical system. These curves provide more information about the system than the zero-dimensional sets (fixed points) do. In fact,…
Real-world problems, for example in climate applications, often require causal reasoning on spatially gridded time series data or data with comparable structure. While the underlying system is often believed to behave similarly at different…
We investigate the algebras of invariants and the properties of the quotient morphism by an action of a finite group scheme in terms of stabilizers of points.
We are interested in dendrites for which all invariant measures of zero-entropy mappings have discrete spectrum, and we prove that this holds when the closure of the endpoint set of the dendrite is countable. This solves an open question…
Machine learning models can assign fixed predictions that preclude individuals from changing their outcome. Existing approaches to audit fixed predictions do so on a pointwise basis, which requires access to an existing dataset of…
Entropy is one of the key thermodynamic variables reflecting changes in the state of matter. Unlike other thermodynamic variables, it is well-defined also for nonequilibrium steady states through its relation to information. Applying this…
An argument is given to associate integrable nonintegrable transition of discrete maps with the transition of Lawvere's fixed point theorem to its own contrapositive. We show that the classical description of nonlinear maps is neither…
In this paper we provide an extension for the method of Discrete Lagrangian Descriptors with the purpose of exploring the phase space of unbounded maps. The key idea is to construct a working definition, that builds on the original approach…
We study proximal random dynamical systems of homeomorphisms of the circle without a common fixed point. We prove the existence of two random points that govern the behavior of the forward and backward orbits of the system. Assuming the…
While the notion of chaos is well established for dynamical systems on manifolds, it is not so for dynamical systems over discrete spaces with $ N $ variables, as binary neural networks and cellular automata. The main difficulty is the…
We present a novel way to apply the singularity confinement property as a discrete integrability criterion. We shall use what we call a full deautonomisation approach, which consists in treating the free parameters in the mapping as…
Determinantal point processes have arisen in diverse settings in recent years and have been investigated intensively. We study basic combinatorial and probabilistic aspects in the discrete case. Our main results concern relationships with…
We consider some smooth maps on a bouquet of circles. For these maps we can compute the number of fixed points, the existence of periodic points and an exact formula for topological entropy. We use Lefschetz fixed point theory and actions…
For any dynamical system $T:X\rightarrow X$ of a compact metric space $X$ with $g-$almost product property and uniform separation property, under the assumptions that the periodic points are dense in $X$ and the periodic measures are dense…
Causal phenomena associated with rare events occur across a wide range of engineering problems, such as risk-sensitive safety analysis, accident analysis and prevention, and extreme value theory. However, current methods for causal…
Researchers in explainable artificial intelligence have developed numerous methods for helping users understand the predictions of complex supervised learning models. By contrast, explaining the $\textit{uncertainty}$ of model outputs has…
Dynamical systems generated by $d\ge2$ commuting homeomorphisms (topological $\mathbb{Z}^d$-actions) contain within them structures on many scales, and in particular contain many actions of $\mathbb{Z}^k$ for $1\le k\le d$. Familiar…
This article aims to investigate sufficient conditions for the stability of stochastic differential equations with a random structure, particularly in contexts involving the presence of concentration points. The proof of asymptotic…