Related papers: A note on an open conjecture in rational dynamical…
We study structural limitations of purely algebraic reasoning in the analysis of arithmetic dynamical systems. Rather than addressing the truth of specific conjectures, we introduce a fragment - relative notion of algebraic refutability for…
To extend the classical concept of Markovianity to an open quantum system, different notions of the divisibility of its dynamics have been introduced. Here we analyze this issue by five complementary approaches: equations of motion,…
We study periodic points for endomorphisms $\sigma$ of abelian varieties $A$ over algebraically closed fields of positive characteristic $p$. We show that the dynamical zeta function $\zeta_\sigma$ of $\sigma$ is either rational or…
The notion of lambda-symmetries, originally introduced by C. Muriel and J.L. Romero, is extended to the case of systems of first-order ODE's (and of dynamical systems in particular). It is shown that the existence of a symmetry of this type…
We prove that, for any real $\lambda$, the system $-\Delta u +\lambda u = u^3-\beta uv^2$, $ -\Delta v+\lambda v =v^3-\beta vu^2$, $ u,v\in H^1_0(\Omega),$ where $\Omega$ is a bounded smooth domain of $R^3$, admits a bounded family of…
We consider the dynamics of particle systems where the particles are confined by impenetrable barriers to a bounded, possibly non-convex domain $\Omega$. When particles hit the boundary, we consider an instant change in velocity, which…
In this survey, we present in a unified way the categorical and syntactical settings of coherent differentiation introduced recently, which shows that the basic ideas of differential linear logic and of the differential lambda-calculus are…
How many free variables do we really need to build a credible model of a physical system? Currently there is no systematic approach; we appeal to some physical principles, tune free variables by comparing with canonical cases, and hope our…
The dominant theories of rational choice assume logical omniscience. That is, they assume that when facing a decision problem, an agent can perform all relevant computations and determine the truth value of all relevant logical/mathematical…
Researchers have started using LLM agents in place of human subjects in behavioural and political-science experiments, often as a cheaper substitute for laboratory pools. The substitution does not hold up in strategic settings: humans and…
An open problem in numerical analysis is to explain why molecular dynamics works. The difficulty is that numerical trajectories are only accurate for very short times, whereas the simulations are performed over long time intervals. It is…
Thermodynamical arguments are known to be useful in the construction of physically motivated Lyapunov functionals for nonlinear stability analysis of spatially homogeneous equilibrium steady states in thermodynamically isolated systems.…
A novel approach is proposed to characterize the dynamics of perturbed many-body integrable systems. Focusing on the paradigmatic case of the Toda chain under non-integrable Hamiltonian perturbations, this study introduces a method based…
Dynamical systems are abstract models of interaction between space and time. They are often used in fields such as physics and engineering to understand complex processes, but due to their general nature, they have found applications for…
In this paper, we consider the following elliptic Toda system associated to a general simple Lie algebra with multiple singular sources \begin{equation*} \begin{cases} -\Delta…
Let $(X,d)$ be a compact metric space and $f:X \to X$ be a self-map. The compact dynamical system $(X,f)$ is called sensitive or sensitivity depends on initial conditions, if there is a positive constant $\delta$ such that in each non-empty…
Systems that exhibit complex behaviours are often found in a particular dynamical condition, poised between order and disorder. This observation is at the core of the so-called criticality hypothesis, which states that systems in a…
We complete the verification of the 1952 Yang and Lee proposal that thermodynamic singularities are exactly the limits in ${\mathbb R}$ of finite-volume singularities in ${\mathbb C}$. For the Ising model defined on a finite…
We introduce a discrete dynamical system on the integers, defined by moving a composite $m$ forward to $m+\pi(m)$ and a prime $p$ backward to $p-\mathrm{prevprime}(p)$. This map produces trajectories whose contraction properties are closely…
In this study, we consider three dark energy models in which $\Lambda$ is not constant, but has a dynamic nature that depends on the Hubble parameter $H$ and/or its time derivative $\dot{H}$. We analyze the generalized running vacuum model,…