arXiv subjects

Jorge Buescu

Publications and source records attributed to Jorge Buescu.

10 recordsLinked to original sources

arXiv2026

Evolutionary Entropy Shapes Lifespan of the Greenland Shark

The Greenland shark (Somniosus microcephalus) is among the longest-lived vertebrates known, with female maturity estimated at about 156 years and maximum ages approaching four centuries. We use the entropic theory of life histories and an open-group Leslie model to determine which reproductive windows are compatible with this extreme demographic profile. The model yields generation times, reproductive quantiles and entropy-maximizing reproductive endpoints. A critical value of reproductive persistence, approximately 0.9763, separates two regimes: below it, evolutionary entropy increases towards an asymptote; above it, entropy is maximized at a finite reproductive endpoint. Longevity-calibrated scenarios lie on both sides of this threshold and imply generation times near or above two centuries, with reproductive contributions extending into the third, fourth and fifth centuries of life. As an independent benchmark, an empirically parametrized Leslie model for the bowhead whale yields comparable entropy-based demographic quantities while allowing the reproductive and survivorship parameters to be calculated directly. The method provides quantitative constraints on reproductive organisation in exceptionally long-lived species for which detailed demographic data are unavailable.

q-bio.PE↗

arXiv2026

Evolutionary Entropy Shapes Reproductive Lifespan in Age-Structured Populations

Evolutionary entropy measures the temporal organization of reproductive contributions along the life cycle of an age-structured population. We develop a mathematical and empirical framework showing that, in iteroparous animal populations represented by Leslie-type demographic matrices, reproductive windows are frequently organized near the age classes selected by entropy maximization. Evolutionary entropy complements the classical net reproductive number and asymptotic growth rate: whereas these measure lifetime replacement and growth, entropy measures the temporal dispersion of the growth-adjusted reproductive distribution. Our central result is a reduction principle: under Euler--Lotka normalization, evolutionary entropy and generation time are invariant under multiplicative rescaling of survivorship and fertility on the reproductive interval. The relevant entropy is determined not by absolute survivorship, fertility, or juvenile mortality, but by the normalized post-maturity reproductive distribution. We derive explicit entropy functionals for finite and open-group Leslie models, including geometric reproductive tails. For the geometric regime, governed by we prove a sharp critical threshold separating populations with a unique finite entropy-maximizing endpoint from those whose entropy increases toward an asymptotic value in terms solely of the age at first reproduction. The theory is tested on 130 animal species. Entropy-derived predictions, computed from the demographic matrices alone, are compared with independent life-history variables. Predicted and observed reproductive medians coincide exactly for a majority of species, over 90% are predicted within three reproductive classes, and associations remain strong after phylogenetic correction. These results identify a quantitative regularity across taxa, with geometric reproductive distributions playing a central role.

q-bio.PE↗

arXiv2026

Laplace measure transitions and ghosts for meromorphic functions

We study the measure transition problem for bilateral Laplace transforms of meromorphic functions on vertical strips. Given a meromorphic function F admitting Laplace representations on two adjacent strips separated by a vertical line, we investigate how the corresponding determining measures are related. Our first result shows that in the absence of poles on the separatrix the determining measures coincide. We next derive explicit transition formulas for the case of finitely many poles and obtain sufficient conditions under which these formulas remain valid for infinitely many poles. Applications are given to the analytic continuation of the zeta function, periodic and almost periodic functions, and quotients of Gamma functions related to the confluent hypergeometric function. Finally, using generalized Cauchy integrals, we construct an entire function admitting distinct Laplace representations on the right and left half-planes, thereby producing a ghost transition. This provides a counterexample to uniqueness of solutions of the Cauchy problem for the heat equation.

math.CV↗

arXiv2025

Lyapunov functions for Morse-Smale synchronisation diffeomorphisms

This paper investigates the dynamical system governing the phase differences between three identical oscillators arranged symmetrically and coupled by burst interactions. By constructing a discrete Lyapunov function, we prove the existence of two asymptotically stable fixed points on the 2-torus T^2, which correspond to Huygens synchronisation of three clocks. The locked states have phase differences of (2 pi/3,4 pi/3) and (4 pi/3,2 pi/3). Each fixed point possesses an open basin of attraction. The closure of the union of the basins of attraction of the two asymptotically stable attractors is the torus T^2, implying that Huygens synchronisation occurs generically and with full Lebesgue measure with respect to initial conditions.

math.DS↗

arXiv2025

A Lyapunov function for a Synchronisation diffeomorphism of three clocks

Lyapunov functions are essential tools in dynamical systems, as they allow the stability analysis of equilibrium points without the need to explicitly solve the system's equations. Despite their importance, no systematic method exists for constructing Lyapunov functions. In a previous paper, we examined a diffeomorphism arising from the problem of Huygens Synchronisation for three identical limit cycle clocks arranged in a line, proving that the system possesses a unique asymptotically stable fixed point on the torus T2, corresponding to synchronisation in phase opposition. In this paper, we re-derive this result by constructing a discrete Lyapunov function for the system. The closure of the basin of attraction of the asymptotically stable attractor is the torus T2, showing that Huygens Synchronisation exhibits generic and robust behaviour, occurring with probability one with respect to initial conditions.

math.DS↗

arXiv2024

Huygens Synchronization of Three Aligned Clocks

This study examines the synchronization of three identical oscillators arranged in an array and coupled by small impacts, wherein each oscillator interacts solely with its nearest neighbor. The synchronized state, which is asymptotically stable, is characterized by phase opposition among alternating oscillators. We analyze the system using a non-linear discrete dynamical system based on a difference equation derived from the iteration of a plane diffeomorphism. We illustrate these results with the application to a system of three aligned Andronov clocks, showcasing their applicability to a broad range of oscillator systems.

math.DS↗

arXiv2018

Propagation of regularity and positive definiteness: a constructive approach

We show that, for positive definite kernels, if specific forms of regularity (continuity, Sn-differentiability or holomorphy) hold locally on the diagonal, then they must hold globally on the whole domain of positive-definiteness. This local-to-global propagation of regularity is constructively shown to be a consequence of the algebraic structure induced by the non-negativity of the associated bilinear forms up to order 5. Consequences of these results for topological groups and for positive definite and exponentially convex functions are explored.

math.CV↗

arXiv2018

Positive-definiteness and integral representations for special functions

We characterize a holomorphic positive definite function $f$ defined on a horizontal strip of the complex plane as the Fourier-Laplace transform of a unique exponentially finite measure on $\mathbb{R}$. The classical theorems of Bochner on positive definite functions and of Widder on exponentially convex functions become special cases of this characterization: they are respectively the real and pure imaginary sections of the complex integral representation. We apply this representation to special cases, including the $Γ$, $ζ$ and Bessel functions, and construct explicitly the corresponding measures, thus providing new insight into the nature of complex positive and co-positive definite functions: in the case of the zeta function this process leads to a new proof of an integral representation on the critical strip.

math.CV↗

arXiv2014

Integral identities derived from the complex Funk-Hecke formula

In this paper we derive integral identities involving both the unit sphere and the unit disk or subsets thereof. In addition these identities lead to a prototype of the Funk-Hecke formula for subspheres embedded in $Ω_{2q}$. The technique requires the use of the complex Funk-Hecke formula, where eigenvalues of the integral operator generated by a bizonal kernel on the unit sphere $Ω_{2q}$ of $\mathbb{C}^q$ are given by an integral on the closed unit disk $B_q$ of $\mathbb{C}^{q-1}$.

math.CV↗

arXiv2011

Computability, Noncomputability, and Hyperbolic Systems

In this paper we study the computability of the stable and unstable manifolds of a hyperbolic equilibrium point. These manifolds are the essential feature which characterizes a hyperbolic system. We show that (i) locally these manifolds can be computed, but (ii) globally they cannot (though we prove they are semi-computable). We also show that Smale's horseshoe, the first example of a hyperbolic invariant set which is neither an equilibrium point nor a periodic orbit, is computable.

math.LO↗