2026-06-23
17:12 |
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15 p, 644.6 KB |
Plane Curves with Proportional Affine and Euclidean Curvatures
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Garcia, Ronaldo A. (Universidade Federal de Goiás. Instituto de Matemática e Estatística) ;
Gasull, Armengol (Universitat Autònoma de Barcelona. Department de Matemàtiques)
In this paper, we obtain all the locally convex plane curves with proportional curvatures (Euclidean and affine). The analysis is performed from a special second order differential equation that, in appropriated coordinates, and using the support function the problem is reduced to the properties of a periodic linear nonhomogeneous second differential equation of the type y'' + y = a (t), a (t + 2π) = a (t).
2026 -  10.1007/s12346-026-01475-3
Qualitative theory of dynamical systems, Vol. 25, Num. 2 (April 2026) , art. 59
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2026-06-23
18:13 |
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2026-06-23
19:13 |
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18 p, 2.8 MB |
New lower bound for the Hilbert number in low degree Kolmogorov systems
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Romano Carvalho, Yagor (Universidade de São Paulo) ;
Da Cruz, Leonardo Pereira Costa (Universidade de São Paulo) ;
Gouveia, Luiz Fernando (Universidade Estadual Paulista "Júlio de Mesquita Filho")
Our main goal in this paper is to study the number of small-amplitude isolated periodic orbits, so-called limit cycles, surrounding only one equilibrium point a class of polynomial Kolmogorov systems. [...]
2023 - 10.1016/j.chaos.2023.113937
Chaos, solitons and fractals, Vol. 175, Num. Part 1 (October 2023) , art. 113937
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2026-06-23
20:13 |
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11 p, 483.0 KB |
Dynamics of two-level laser models with cavity loss modulation and delayed feedback
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Meucci, Riccardo (Consiglio Nazionale Delle Ricerche. Istituto Nazionale di Ottica) ;
Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ;
Pugliese, Eugenio (Consiglio Nazionale Delle Ricerche. Istituto Nazionale di Ottica) ;
Ginoux, Jean-Marc (Centre National de la Recherche Scientifique. Aix Marseille University. Université de Toulon)
In 1982, Arecchi et al. [Phys. Rev. Lett. 49, 1217 (1982)] proposed a simple two-level laser model to interpret the first evidence of chaos and generalized multistability in a Q-switched CO laser. [...]
2023 - 10.1364/JOSAB.493375
Journal of the Optical Society of America B: Optical Physics, Vol. 40, Num. 8 (August 2023) , p. 2114-2121
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2026-03-05
16:16 |
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2026-03-05
08:14 |
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2026-03-05
08:14 |
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29 p, 2.2 MB |
On the integrability and dynamics of the Hide, Skeldon and Acheson differential system
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Diz-Pita, Érika (Universidade de Santiago de Compostela. Departamento de Estatística, Análise Matemática e Optimización) ;
Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ;
Otero-Espinar, M. Victoria (Universidade de Santiago de Compostela. Departamento de Estatística, Análise Matemática e Optimización) ;
Valls, Clàudia 1973- (Universidade de Lisboa. Instituto Superior Técnico. Departamento de Matemática)
The family of systems x˙ = x(y - 1) - βz, y˙ = α(1 - x2) - κy, z˙ = x - λz, where (x, y, z) ∈ R3 and α, β, κ, λ are real parameters, was proposed by Hide, Skeldon and Acheson in 1996 for the study of self-excited dynamo action in which a Faraday disc and coil are arranged in series with either a capacitor or a motor. [...]
2025 - 10.14232/ejqtde.2025.1.76
Electronic Journal of Qualitative Theory of Differential Equations, Num. 76 (2025) , p. 1-29
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2026-02-26
19:12 |
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18 p, 1.6 MB |
The Easiest Polynomial Differential Systems in ℝ 3 Having an Invariant Hyperboloid
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Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ;
Salhi, Tayeb (University Mohamed El Bachir El Ibrahimi. Department of Mathematics)
This paper answers the following two questions: What are the easiest polynomial differential systems in ℝ3 having an invariant hyperboloid of one sheet, or an invariant hyperboloid of two sheets? And, for this kind of polynomial differential systems, what are their phase portraits on such an invariant hyperboloids? To solve these questions, a method based on first integrals, symmetry, analysis of the nature of equilibrium points, and invariant algebraic surfaces is employed.
2025 - 10.1142/S0218127425501391
International journal of bifurcation and chaos in applied sciences and engineering, Vol. 35, Num. 12 (September 2025) , art. 2550139
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2026-02-26
19:12 |
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2026-02-26
17:12 |
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44 p, 1.8 MB |
Characterization of the tree cycles with minimum positive entropy for any period
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Juher, David (Universitat de Girona) ;
Mañosas, Francesc (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ;
Rojas, David (Universitat Autònoma de Barcelona. Departament de Matemàtiques)
Consider, for any integer n ≥ 3, the set Posn of all n-periodic tree patterns with positive topological entropy and the set Irrn⊂Posn of all n-periodic irreducible tree patterns. The aim of this paper is to determine the elements of minimum entropy in the families Posn, Irrn and Posn∖Irrn. [...]
2025 - 10.1017/etds.2025.11
Ergodic Theory and Dynamical Systems, Vol. 45, Num. 10 (October 2025) , p. 3148-3191
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