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Mather β-Function for Ellipses and Rigidity
Entropy, 2022 The goal of the first part of this note is to get an explicit formula for rotation number and Mather β-function for ellipse. This is done here with the help of non-standard generating function of billiard problem. In this way the derivation is especially
Michael Bialy
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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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Synchronization of coupled generators of quasi-periodic oscillations upon destruction of invariant curve [PDF]
Известия высших учебных заведений: Прикладная нелинейная динамика, 2021 The purpose of this study is to describe the complete picture of synchronization of two coupled generators of quasi-periodic oscillations, to classify various types of synchronization, to study features of occurrence and destruction of multi-frequency ...
Kuznetsov, Aleksandr Petrovich +2 more
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Size invariance in curve tracing [PDF]
Memory & Cognition, 1991 Subjects decided whether two dots were on the same curve or on different curves in patterns consisting of two curves and two dots in displays that had an exposure duration of 200 msec or that remained in view until the subjects' response. The overall size of the patterns was varied by a factor of two. Furthermore, across experiments, we manipulated the
P, Jolicoeur, M, Ingleton
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LOCAL SYMPLECTIC INVARIANTS FOR CURVES [PDF]
Communications in Contemporary Mathematics, 2009 We consider curves in ℝ2n endowed with the standard symplectic structure. We introduce the concept of symplectic arc length for curves. We construct an adapted symplectic Frenet frame and we define 2n - 1 local differential invariants that we call symplectic curvatures of the curve.
Kamran, Niky +2 more
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Polynomial differential systems with hyperbolic algebraic limit cycles
Electronic Journal of Qualitative Theory of Differential Equations, 2020 For a given algebraic curve of degree $n$, we exhibit differential systems of degree greater than or equal $n$, by introducing functions which are solutions of certain partial differential equations.
Salah Benyoucef
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E-strings, F 4, and D 4 triality
Journal of High Energy Physics, 2023 We study the E-string theory on ℝ4 × T 2 with Wilson lines. We consider two examples where interesting automorphisms arise. In the first example, the spectrum is invariant under the F 4 Weyl group acting on the Wilson line parameters.
Kazuhiro Sakai
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Machine learning invariants of arithmetic curves [PDF]
Journal of Symbolic Computation, 2023 In the present paper, the authors show that an machine learning classifier can be trained to predict the rank and the torsion order of an elliptic curve or a genus two curve with high precision when the curve is represented by a few hundred coefficients of its \(L\)-function.
He, Y-H., Lee, K-H., Oliver, T.
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Stability of a certain class of a host–parasitoid models with a spatial refuge effect
Journal of Biological Dynamics, 2020 A certain class of a host–parasitoid models, where some host are completely free from parasitism within a spatial refuge is studied. In this paper, we assume that a constant portion of host population may find a refuge and be safe from attack by ...
E. Bešo +3 more
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Cascade of Invariant Curve Doubling Bifurcations and Quasi-Periodic Hénon Attractor in the Discrete Lorenz-84 Model [PDF]
Известия Саратовского университета. Новая серия: Физика, 2020 Background and Objectives: Chaotic behavior is one of the fundamental properties of nonlinear dynamical systems, including maps. Chaos can be most easily and reliably diagnosed using the largest Lyapunov exponent, which will be positive for the chaotic ...
Popova, Elena Sergeevna +2 more
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