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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2026-02-26
16:20 |
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36 p, 1.1 MB |
Entropy stability and Milnor-Thurston invariants for Bowen-Series-like maps
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Alsedà, Lluís (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ;
Juher, David (Universitat de Girona. Departament d'Informàtica i Matemàtica Aplicada) ;
Los, Jérôme (Aix-Marseille Université. Institut de Mathématiques de Marseille) ;
Mañosas, Francesc (Universitat Autònoma de Barcelona. Departament de Matemàtiques)
We define a family of discontinuous maps on the circle, called Bowen-Series-like maps, for geometric presentations of surface groups. The family has 2N parameters, where 2N is the number of generators of the presentation. [...]
2026 - 10.1017/etds.2025.10245
Ergodic Theory and Dynamical Systems, Vol. 46, Num. 2 (February 2026) , p. 337-372
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2026-02-25
20:12 |
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2026-02-25
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2026-02-25
19:12 |
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9 p, 322.1 KB |
Limit cycles of a class of hybrid piecewise differential systems with a discontinuity line of L shape
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Anacona Cabrera, Marly Tatiana (Universidade Federal de Goiás. Instituto de Matemática e Estatística) ;
Anacona Erazo, Gerardo (Universidade Federal de Goiás. Instituto de Matemática e Estatística) ;
Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques)
In this work we study a class of discontinuous hybrid piecewise differential systems formed by two linear Hamiltonian systems that we named piecewise hybrid Hamiltonian systems. More precisely, we consider the differential systems with Hamiltonian functions H1(x, y) = a1x + a2y + a3x2 + a4xy + a5y2 + A, H2(x,y) = b1x + a2y + b3x2 + b4xy + b5y2 + B, if (x, y) ∈ Σ + if (x, y) ∈ Σ- with reset maps R1(x) = sx on x ≥ 0 and R2(y) = ry ony ≥ 0for0 < r,s < 1, and A, B are either zero, or one of them is a nonzero homogeneous polynomial of degree 3, Σ + = {(x, y) ∈ R2 : x ≥ 0 and y ≥ 0} and Σ- is the closure of R2 \Σ+. [...]
2026 - 10.1016/j.nonrwa.2025.104492
Nonlinear Analysis: Real World Applications, Vol. 88 (April 2026) , art. 104492
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