math.DS papers | Gist.Science

Generic twisted Pollicott--Ruelle resonances and zeta function at zero

This paper establishes that for a generic set of finite-dimensional irreducible representations of the fundamental group of a surface's unit tangent bundle, the twisted Ruelle zeta function either vanishes at zero with an order determined by the genus or equals the Reidemeister--Turaev torsion, thereby extending Fried's conjecture to generic acyclic representations and confirming the constancy of the vanishing order for untwisted zeta functions across a dense set of Anosov metrics.

Tristan Humbert, Zhongkai Tao2026-03-05🔢 math

Duffin--Schaeffer examples, real residue systems, and Bohr-set primes

This paper generalizes the Duffin–Schaeffer theorem to real residue systems by establishing a zero-one law for inhomogeneous approximation based on the parameter's membership in specific sets, utilizing novel results on the distribution of primes in Bohr sets and the equidistribution of circle rotations.

Stefan M. Hesseling, Felipe A. Ramirez2026-03-05🔢 math

Internet malware propagation: Dynamics and control through SEIRV epidemic model with relapse and intervention

This paper proposes an SEIRV epidemic model with relapse and intervention to analyze malware propagation dynamics, establish stability conditions, identify key influencing parameters, and optimize cost-effective control strategies using a hybrid gradient-based framework calibrated with real-world infection data.

Samiran Ghosh, V Anil Kumar2026-03-05🔢 math

A variational principle for holomorphic correspondences

This paper establishes a variational principle for holomorphic correspondences on the Riemann sphere by defining their measure-theoretic entropy and using it to formulate the pressure of continuous functions, analogous to the theory for continuous maps on compact metric spaces.

Subith Gopinathan, Shrihari Sridharan2026-03-05🔢 math

Equi-Baire One Families of Möbius Transformations and One-Parameter Subgroups of $\mathrm{PSL}(2,\mathbb{C}$ )

This paper investigates the Equi-Baire one property for families of Möbius transformations, demonstrating that iterates of loxodromic maps form such a family on their attracting basins and establishing that a one-parameter subgroup satisfies this condition on all compact sets if and only if it is relatively compact in $\mathrm{SL}(2,\mathbb{C})$ .

Sandipan Dutta, Vanlalruatkimi, Jonathan Ramdikpuia2026-03-05🔢 math

Steady State Distribution and Stability Analysis of Random Differential Equations with Uncertainties and Superpositions: Application to a Predator Prey Model

This paper presents a Monte Carlo-based computational framework to analyze the steady-state distributions and stability of random differential equations with uncertain, multi-modal parameters, demonstrating its efficacy through a Rosenzweig-MacArthur predator-prey model that reveals complex, multi-modal equilibrium behaviors.

Wolfgang Hoegele2026-03-05🔢 math

Topological-numerical analysis of global dynamics in the discrete-time two-gene Andrecut-Kauffman model

This paper employs rigorous topological-numerical methods, specifically Morse decomposition and Conley index computations, to analyze the global dynamics of a discrete-time two-gene Andrecut-Kauffman model, revealing complex phenomena such as multistability and chaotic attractors across a wide range of parameters.

Dorian Falęcki, Mikołaj Rosman, Michał Palczewski + 2 more2026-03-05🔢 math

Lubin's conjecture for height-one $p$ -adic dynamical systems over $(p^2-p)$ -tame extensions

This paper proves Lubin's conjecture in new cases by demonstrating that over $(p^2-p)$ -tame extensions, the consistent sequences associated with a commuting pair of noninvertible and invertible height-one formal power series form a crystalline character of weight 1.

Martin Debaisieux2026-03-05🔢 math

On Cauchy problem and stability of inversion-free feedforward control of piecewise monotonic Krasnoselskii-Pokrovskii hysteresis

This paper establishes the existence, uniqueness, boundedness, and global stability of solutions for a Cauchy problem involving a non-homogeneous first-order differential equation with Krasnoselskii-Pokrovskii hysteresis, specifically analyzing its application to inversion-free feedforward control in magnetic shape memory alloy actuators through theoretical theorems and numerical examples.

Jana Kopfova, Michael Ruderman2026-03-05🔢 math

Competitive tumor growth modeling and optimal radiotherapy control via logistic equations

This paper develops and analyzes mathematical models based on logistic equations and the Linear Quadratic model to demonstrate how optimal control theory can improve radiotherapy strategies by reducing tumor burden while minimizing damage to healthy tissue compared to constant radiation approaches.

Javier López-Pedrares, Alba López-Rivas, Raquel Romero-Lorenzo + 2 more2026-03-05🔢 math

Electric current dynamics in the stellarator coil winding surface model

This paper establishes a theoretical framework for stellarator coil winding surfaces that proves a dichotomy principle for current distributions on toroidal shapes and demonstrates that oppositely oriented currents on piecewise cylindrical surfaces generate center and saddle point regions with predominantly periodic field lines, offering key insights for optimizing coil design.

Wadim Gerner, Anouk Nicolopoulos-Salle, Diego Pereira Botelho2026-03-05🔬 physics

Lyapunov characterization of boundedness of reachability sets for infinite-dimensional systems

This paper establishes a converse Lyapunov theorem for the boundedness of reachability sets in infinite-dimensional systems with Lipschitz continuous flows, demonstrating its applicability to semi-linear evolution equations and deriving a result for forward completeness in ordinary differential equations without restricting input magnitudes.

Patrick Bachmann, Andrii Mironchenko2026-03-05🔢 math

Plane geometry of $q$ -rationals and Springborn Operations

This paper investigates the plane geometry of $q$ -rationals by constructing deformed Farey triangulations and modular surfaces, interpreting these numbers as Ford-like circles, and introducing Springborn operations as quadratic generalizations of Farey addition that correspond geometrically to the homothety centers of circle pairs.

Perrine Jouteur, Olga Paris-Romaskevich, Alexander Thomas2026-03-05🔢 math

A Symmetry-Based Classification of Synchrony in Tree Networks

This paper demonstrates that in tree networks, all synchrony patterns are strictly induced by graph automorphisms rather than exotic mechanisms, and further analyzes how the combinatorial architecture, particularly leaf configurations, governs the linear and Lyapunov stability of these synchronous states.

Nicolas Brito, Miriam Manoel2026-03-05🔢 math

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