Results 1 to 10 of about 383 (129)
Al-Mustansiriyah Journal of Science, 2021 In this paper, we present two gyroarea formulas (Möbius-Bretschneider’s formula and Möbius-Cagnoli’s formula) for Möbius gyroquadrilaterals in the Poincaré disc model of hyperbolic geometry.
Gülcan Balakan, Oğuzhan Demirel
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Global phase portraits of a predator–prey system
Electronic Journal of Qualitative Theory of Differential Equations, 2022 We classify the global dynamics of a family of Kolmogorov systems depending on three parameters which has ecological meaning as it modelizes a predator–prey system.
Érika Diz-Pita +2 more
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The Beckman–Quarles Theorem in Hyperbolic Geometry
Journal of Mathematics, 2021 In this paper, we present the counterpart of the Beckman–Quarles theorem in the Poincaré disc model of hyperbolic geometry to characterize the gyroisometries (hyperbolic isometries) with a single nonzero distance a∈0,1 satisfying a2∈ℚ.
Oğuzhan Demirel +2 more
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Phase Portraits of Families VII and VIII of the Quadratic Systems
Axioms, 2023 The quadratic polynomial differential systems in a plane are the easiest nonlinear differential systems. They have been studied intensively due to their nonlinearity and the large number of applications.
Laurent Cairó, Jaume Llibre
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An Extension of Poincare Model of Hyperbolic Geometry with Gyrovector Space Approach [PDF]
Mathematics Interdisciplinary Research, 2016 The aim of this paper is to show the importance of analytic hyperbolic geometry introduced in [9]. In [1], Ungar and Chen showed that the algebra of the group SL(2, C) naturally leads to the notion of gyrogroups and gyrovector spaces for dealing ...
Mahfouz Rostamzadeh +1 more
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Confocal Families of Hyperbolic Conics via Quadratic Differentials
Axioms, 2023 We apply the theory of quadratic differentials, to present a classification of orthogonal pairs of foliations of the hyperbolic plane by hyperbolic conics.
Joel Langer, David Singer
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Singular points and limit cycles of the generalized Kukles polynomial differential system
Известия высших учебных заведений. Поволжский регион: Физико-математические науки, 2022 Background. Searching of numbers of Poincare limit cycles of polynomial dynamic systems belongs to second part of the 16th Gilbert problem, which is not solved in general.
I.N. Mal'kov, V.V. Machulis
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Demonstratio Mathematica, 2023 The classification of the phase portraits is one of the classical and difficult problems in the qualitative theory of polynomial differential systems in R2{{\mathbb{R}}}^{2}, particularly for quadratic systems.
Benterki Rebiha, Belfar Ahlam
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On the cyclicity of Kolmogorov polycycles
Electronic Journal of Qualitative Theory of Differential Equations, 2022 In this paper we study planar polynomial Kolmogorov's differential systems \[ X_\mu\quad\begin{cases}{\dot{x}=f(x,y;\mu),}\\{\dot{y}=g(x,y;\mu),} \end{cases} \] with the parameter $\mu$ varying in an open subset $\Lambda\subset\mathbb{R}^N ...
David Marín, Jordi Villadelprat
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The Quaternionic Hardy Space and the Geometry of the Unit Ball
Bruno Pini Mathematical Analysis Seminar, 2015 The quaternionic Hardy space of slice regular functions H2(B) is a reproducing kernel Hilbert space. In this note we see how this property can be exploited to construct a Riemannian metric on the quaternionic unit ball B and we study the geometry arising
Giulia Sarfatti
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