arXiv subjects

A. Della Corte

Publications and source records attributed to A. Della Corte.

4 recordsLinked to original sources

arXiv2026

Order spectra in topological dynamical systems

In a compact topological dynamical system $(X,f)$, we associate to every pair $(x,y)$ a canonical order-theoretic invariant, its emergent order spectrum $Ω(x,y)$. We first prove that, if $x$ and $y$ are chain-related, one can always build families of nested and acyclic $\varepsilon_n$-chains ($\varepsilon_n \to 0$). The order spectrum $Ω(x,y)$ is then defined as the set of countable linear order-types obtained as direct limits of (order-compatible) nested and acyclic $\varepsilon_n$-chains. The spectrum is independent of the vanishing sequence and invariant under topological conjugacy, and it refines Conley's partial order.

math.DS↗

arXiv2026

On linearly ordered sets of chain components

In a dynamical system $(X,f)$, with $X$ a compact metric space, the chain components, the fundamental building blocks in the Conley decomposition of dynamics, have a natural partial order induced by the chain relation between points. Although chain components are crucial for understanding the long-term behavior of topological systems, they have not been widely studied from the point of view of poset theory. In this work, we pursue this line of research, considering both the case in which $f$ is a continuous map and the general case in which no regularity assumption is made. Our main results are that, if $f$ is continuous: - the chain components poset cannot be linearly and densely ordered; - every countable well-order with a maximum is the order type of the chain components poset of an interval map. If no regularity assumption is made: - there is a dynamical system on the interval whose chain components poset is countable and densely ordered; - the chain components poset has at least one minimal element. These results, bridging dynamical systems and order theory, highlight both the structural constraints and the possibilities for the chain components posets.

math.DS↗

arXiv2026

A no-go theorem for irreversibility along single-branch collapse dynamics

We study finite dimensional quantum systems with arbitrary collapse events, establishing, under no-information-erasure conditions, a structural no-go for operational irreversibility along single branches of the collapse dynamics. More precisely, we prove that, for every physically admissible selector of the collapse dynamics, there exists a topologically closed, forward-invariant subset of the projective state space on which any two states can be connected with arbitrarily fine Fubini-Study precision and arbitrarily small integrated energetic cost. This shows that the preservation of information along a realized branch of outcomes guarantees islands of quasi-reversibility, while genuine irreversibility requires additional ingredients such as non-compactness or information erasure. KEYWORDS: Quantum collapse dynamics; Quasi-reversibility; Chain-recurrence; Information non-erasure.

math-ph↗

arXiv2022

A non-autonomous variational problem describing a nonlinear Timoshenko beam

We study the non-autonomous variational problem: \begin{equation*} \inf_{(ϕ,θ)} \bigg\{\int_0^1 \bigg(\frac{k}{2}ϕ'^2 + \frac{(ϕ-θ)^2}{2}-V(x,θ)\bigg)\text{d}x\bigg\} \end{equation*} where $k>0$, $V$ is a bounded continuous function, $(ϕ,θ)\in H^1([0,1])\times L^2([0,1])$ and $ϕ(0)=0$ in the sense of traces. The peculiarity of the problem is its setting in the product of spaces of different regularity order. Problems with this form arise in elastostatics, when studying the equilibria of a nonlinear Timoshenko beam under distributed load, and in classical dynamics of coupled particles in time-depending external fields. We prove the existence and qualitative properties of global minimizers and study, under additional assumptions on $V$, the existence and regularity of local minimizers.

math.AP↗