Results 1 to 10 of about 54 (53)
Transversal homoclinic points of the Hénon map [PDF]
Annali di Matematica Pura ed Applicata, 2005 ISSN:1618 ...
Kirchgraber, Urs, Stoffer, Daniel
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On the Price Dynamics of a Two-Dimensional Financial Market Model with Entry Levels
Complexity, 2020 This paper aims to extend the model developed by Tramontana et al. By adding trend followers who pay attention to the most recent observed price trend, we formulate a financial market model driven by a new two-dimensional discontinuous piecewise linear ...
En-Guo Gu
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The Existence of Transverse Homoclinic Points in the Sitnikov Problem
Journal of Differential Equations, 1995 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Dankowicz, H., Holmes, P.
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The Transverse Homoclinic Dynamics and their Bifurcations at Nonhyperbolic Fixed Points [PDF]
Transactions of the American Mathematical Society, 1992 The complete description of the dynamics of diffeomorphisms in a neighborhood of a transverse homoclinic orbit to a hyperbolic fixed point is obtained. It is topologically conjugate to a non-Bernoulli shift called { ∑ , σ } \{ {\sum ,\sigma } \} .
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Existence of transversal homoclinic points in a degenerative case
Rocky Mountain Journal of Mathematics, 1990 This interesting paper deals with the periodic differential equation \((1)\quad \dot x=g(x)+\mu h(t,x,\mu),\) where \(x\in {\mathbb{R}}^ k\), \(\mu\in {\mathbb{R}}\), h(t,x,\(\mu\)) is T-periodic in its first variable, and the unperturbed system (2) \(\dot x=g(x)\) has a saddle point \(x_ 0\).
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The transversal homoclinic points are dense in the codimension-1 Hénon-like strange attractors [PDF]
Proceedings of the American Mathematical Society, 1999 We consider the codimension-1 Hénon-like strange attractors Λ \Lambda . We prove that the transversal homoclinic points are dense in Λ \Lambda , and that hyperbolic periodic points are dense in Λ \Lambda .
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Journal of Differential Equations, 2019 It is well-known that chaos arises if a smooth dynamical system which admits a transversal homoclinic point is perturbed. This paper presents a new result that this phenomenon may not exist for some piecewise smooth two-dimensional systems subjected to a periodic or almost periodic perturbation.
M. Franca, M. Pospíšil
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Transversal homoclinic points of a class of conservative diffeomorphisms
Journal of Differential Equations, 1990 Area preserving diffeomorphisms of \({\mathbb{R}}^ 2\) of the form \(F(x,y)=(y,-x+2G(y))\) are considered. In the conservative case \((b=-1)\), the Hénon map is conjugated to F with \(G(y)=y^ 2+cy.\) It is proved, that if \(c>1\) then there exists a homoclinic point \(p_ c\neq (0,0)\) and the angle between the invariant manifolds at \(p_ c\) is an ...
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Melnikov method and transversal homoclinic points in the restricted three-body problem
Journal of Differential Equations, 1992 In this paper we show, by Melnikov method, the existence of the transversal homoclinic orbits in the circular restricted three-body problem for all but some finite number of values of the mass ratio of the two primaries. This implies the existence of a family of oscillatory and capture motion.
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On the existence of transversal homoclinic points of some real analytic plane transformation
Kyoto Journal of Mathematics, 1983 Let f be a plane transformation \(f(x,y)=(y+\xi(x),x),\) where \(\xi(x)\) is a real analytic function satisfying the following conditions: (1) \(\xi(x)=\xi(1-x)\); (2) \(\xi(0)=0\); (3) \(\xi'(x)>0\) for \(x\in(- \infty,\frac{1}{2})\); and (4) \(\xi''(x)0)\) is a particular case.
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