- ItemOpen AccessThe blow-up method applied to monodromic singularities(Bolyai Institute, 2024) Fercec, Brigita; Giné, JaumeThe blow-up method proves its effectiveness to characterize the integrability of the resonant saddles giving the necessary conditions to have formal integrability and the sufficiency doing the resolution of the associated recurrence differential equation using induction. In this work we apply the blow-up method to monodromic singularities in order to solve the center-focus problem. The case of nondegenerate monodromic singularities is straightforward since any real nondegenerate monodromy singularity can be embedded into a complex system with a resonant saddle. Here we apply the method to nilpotent and degenerate monodromic singularities solving the center problem when the center conditions are algebraic
- ItemOpen AccessThe Horizons in Circular Accelerated Motions and Its Consequences(MDPI, 2023) Giné, JaumeIn this work, we study the existence of horizons in circular accelerated motions and its consequences. One particular case is the existence of two horizons in any uniform circular motion. The radiation of the Poincaré invariant vacuum is related to the spontaneous breakdown of the conformal symmetry in Quantum Field Theory The main consequence of the existence of these horizons is the Unruh radiation coming from such horizons. This consequence allows us to study the possible experimental detection of the Unruh radiation in such motions. The radiation of the Poincaré invariant vacuum is related to the spontaneous breakdown of the conformal symmetry in Quantum Field Theory. This radiation is associated with an effective temperature that can be detected using an Unruh–DeWitt detector. In fact, this effective temperature at the relativistic limit depends linearly with respect to the proper acceleration. However, in general, this dependence is not linear, contrary of what happens in the classical Unruh effect. In the relativistic limit and high density case, the uniform circular motion becomes a rotating black hole. This allows for future studies of pre-black hole configurations.
- ItemOpen AccessOn the spectra and spectral radii of token graphs(Springer, 2024-01-06) Reyes, Mònica Andrea; Dalfó, Cristina; Fiol Mora, Miguel ÁngelLet G be a graph on n vertices. The k-token graph (or symmetric k-th power) of G, denoted by Fk(G), has as vertices the (n/k) k-subsets of vertices from G, and two vertices are adjacent when their symmetric difference is a pair of adjacent vertices in G. In particular, Fk(Kn) is the Johnson graph J(n, k), which is a distance-regular graph used in coding theory. In this paper, we present some results concerning the (adjacency and Laplacian) spectrum of Fk(G) in terms of the spectrum of G. For instance, when G is walk-regular, an exact value for the spectral radius (or maximum eigenvalue) of Fk(G) is obtained. When G is distance-regular, other eigenvalues of its 2-token graph are derived using the theory of equitable partitions. A generalization of Aldous’ spectral gap conjecture (which is now a theorem) is proposed.
- ItemOpen AccessTime-reversibility and integrability of p : −q resonant vector fields(AIMS Press, 2024) Giné, Jaume; Romanovski, Valery G.; Torregrosa, JoanWe study the local analytical integrability in a neighborhood of p : −q resonant singular point of a two-dimensional vector field and its connection to time-reversibility with respect to the nonsmooth involution ϕ(x, y) = (y p/q , x q/p). Some generalizations of the theory developed by Sibirsky for the 1 : −1 resonant case to the p : −q resonant case are presented.
- ItemOpen AccessNon-autonomous inverse Jacobi multipliers and periodic orbits of planar vector fields(Elsevier, 2024) García, I. A. (Isaac A.); Maza Sabido, SusannaWe analyze the role that non-autonomous (and not necessarily periodic) inverse Jacobi multipliers have in the problem of the nonexistence, existence and localization as well as the hyperbolic nature of periodic orbits of planar vector fields. This work generalizes and extends previous results already appearing in the literature which are only focusing in the autonomous or periodic case. Therefore we are able to provide novel applications of inverse Jacobi multipliers.