On Shilnikov's scenario in 3D: Topological chaos for vectorfields of class $C^1$
Electronic Journal of Qualitative Theory of Differential EquationsShilnikov's scenario in $\mathbb{R}^3$ means that the equation $x'=V(x)\in\mathbb{R}^3$ with $V(0)=0$ has a homoclinic solution and the eigenvalues of $DV(0)$ are $u>0$ and $\sigma\pm i\mu$ with ...
Hans-Otto Walther
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Modulational instability and homoclinic orbit solutions in vector nonlinear Schrödinger equation [PDF]
Communications in nonlinear science & numerical simulation, 2017 Liming Ling, Li-Chen Zhao
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Exploring the Influence of Oblateness on Asymptotic Orbits in the Hill Three-Body Problem
AppliedMathWe examine the modified Hill three-body problem by incorporating the oblateness of the primary body and focus on its asymptotic orbits. Specifically, we analyze and characterize homoclinic and heteroclinic connections associated with the collinear ...
Vassilis S. Kalantonis
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On Two-Dimensional Diffeomorphisms with Homoclinic Orbits to Nonhyperbolic Fixed Points [PDF]
, 2023 С. В. Гонченко +1 more
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Homoclinic orbits in 3D dissipative systems [PDF]
Scientific Technical Review, 2014 The paper deals with a variational system corresponding to a three-dimensional dynamic system. The characteristic equation of the variational system depends on partial solutions. The matrix of the right-hand part of the variational system is a sum of two
Martynyuk Andreevich Anatoly +1 more
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Homoclinic orbits for a class of $p$-Laplacian systems with periodic assumption
Electronic Journal of Qualitative Theory of Differential Equations, 2013 In this paper, by using a linking theorem, some new existence criteria of homoclinic orbits are obtained for the $p$-Laplacian system $d(|\dot{u}(t)|^{p-2}\dot{u}(t))/dt+\nabla V(t,x)=f(t)$, where $p>1$, $V(t,x)=-K(t,x)+W(t,x)$.
Xingyong Zhang
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Periodic or homoclinic orbit bifurcated from a heteroclinic loop for high-dimensional systems
Open MathematicsConsider an autonomous ordinary differential equation in Rn{{\mathbb{R}}}^{n}, which has a heteroclinic loop. Assume that the heteroclinic loop consists of two degenerate heteroclinic orbits γ1{\gamma }_{1}, γ2{\gamma }_{2} and two saddle points with ...
Long Bin, Yang Yiying
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Analytical study of the Lorenz system: Existence of infinitely many periodic orbits and their topological characterization. [PDF]
Proc Natl Acad Sci U S A, 2023 Pinsky T.
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Homoclinic orbits for discrete Hamiltonian systems with subquadratic potential [PDF]
, 2013 Xiaoyan Lin, Xianhua Tang
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