29 citations · 78 across the 12 of their papers we have counts for
12 papers
Bounding the number of limit cycles in piecewise linear differential systems: methodology and worked examples
Victoriano Carmona, Fernando Fernández-Sánchez, Douglas D. Novaes
In 2012, Huan and Yang introduced the first piecewise linear differential system with two zones separated by a straight line having at least three limit cycles, serving as a counte…
A succinct characterization of period annuli in planar piecewise linear differential systems with a straight line of nonsmoothness
Victoriano Carmona, Fernando Fernández-Sánchez, Douglas D. Novaes
We close the problem of the existence of period annuli in planar piecewise linear differential systems with a straight line of nonsmoothness. In fact, a characterization for the ex…
Uniform upper bound for the number of limit cycles of planar piecewise linear differential systems with two zones separated by a straight line
Victoriano Carmona, Fernando Fernández-Sánchez, Douglas D. Novaes
The existence of a uniform upper bound for the maximum number of limit cycles of planar piecewise linear differential systems with two zones separated by a straight line has been s…
Strictification theorems for the homotopy time-slice axiom
Marco Benini, Victor Carmona, Alexander Schenkel
It is proven that the homotopy time-slice axiom for many types of algebraic quantum field theories (AQFTs) taking values in chain complexes can be strictified. This includes the ca…
Uniqueness and stability of limit cycles in planar piecewise linear differential systems without sliding region
Victoriano Carmona, Fernando Fernández-Sánchez, Douglas D. Novaes
In this paper, we consider the family of planar piecewise linear differential systems with two zones separated by a straight line without sliding regions, that is, differential sys…
When Bousfield localizations and homotopy idempotent functors meet again
Victor Carmona
We adopt semimodel categories to extend fundamental results related to Bousfield localizations of model categories. More specifically, we generalize Bousfield-Friedlander Theorem a…
Properties of Poincaré half-maps for planar linear systems and some direct applications to periodic orbits of piecewise systems
Victoriano Carmona, Fernando Fernández-Sánchez, Elisabeth García-Medina +1
This paper deals with fundamental properties of Poincaré half-maps defined on a straight line for planar linear systems. Concretely, we focus on the analyticity of the Poincaré hal…
New model structures for Algebraic Quantum Field Theory
Victor Carmona
In this paper we define and compare several new Quillen model structures which present the homotopy theory of algebraic quantum field theories. In this way, we expand foundational…
A model structure for locally constant factorization algebras
Victor Carmona, Ramon Flores, Fernando Muro
Several model structures related to the homotopy theory of locally constant factorization algebras are constructed. This answers a question raised by D. Calaque in his habilitation…
Saddle-node canard cycles in planar piecewise linear differential systems
Victoriano Carmona, Soledad Fernández-García, Antonio E. Teruel
By applying a singular perturbation approach, canard limit cycles exhibited by a general family of singularly perturbed planar piecewise linear (PWL) differential systems are analy…
A new simple proof for Lum-Chua's conjecture
Victoriano Carmona, Fernando Fernández-Sánchez, Douglas D. Novaes
The already proved Lum-Chua's conjecture says that a continuous planar piecewise linear differential system with two zones separated by a straight line has at most one limit cycle.…
Integral characterization for Poincaré half-maps in planar linear systems
Victoriano Carmona, Fernando Fernández-Sánchez
The intrinsic nature of a problem usually suggests a first suitable method to deal with it. Unfortunately, the apparent ease of application of these initial approaches may make the…