Results 101 to 110 of about 9,394 (211)
A Note on Homoclinic Orbits for Second Order Hamiltonian Systems [PDF]
, 2014 In this paper, we study the existence for the homoclinic orbits for the second order Hamiltonian systems. Under suitable conditions on the potential $V$, we apply the direct method of variations and the Fourier analysis to prove the existence of ...
Li, Bingyu +3 more
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Dominated Pesin theory: convex sum of hyperbolic measures
, 2017 In the uniformly hyperbolic setting it is well known that the set of all measures supported on periodic orbits is dense in the convex space of all invariant measures.
Bochi, Jairo +2 more
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Homoclinic orbits of second-order nonlinear difference equations
Electronic Journal of Differential Equations, 2015 We establish existence criteria for homoclinic orbits of second-order nonlinear difference equations by using the critical point theory in combination with periodic approximations.
Haiping Shi, Xia Liu, Yuanbiao Zhang
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On periodic solutions in the non-dissipative Lorenz model: the role of the nonlinear feedback loop
Tellus: Series A, Dynamic Meteorology and Oceanography, 2018 In this study, we discuss the role of the linear heating term and nonlinear terms associated with a non-linear feedback loop in the energy cycle of the three-dimensional (X–Y–Z) non-dissipative Lorenz model (3D-NLM), where (X, Y, Z) represent the ...
B.-W. Shen
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Shil'nikov Chaos control using Homoclinic orbits and the Newhouse region
, 2006 A method of controlling Shil'nikov's type chaos using windows that appear in the 1 dimensional bifurcation diagram when perturbations are applied, and using existence of stable homoclinic orbits near the unstable one is presented and applied to the ...
Furui, Sadataka, Niiya, Shohei
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A Numerical Bifurcation Function for Homoclinic Orbits
SIAM Journal on Numerical Analysis, 1998 Summary: The authors present a numerical method to locate periodic orbits near homoclinic orbits. Using a method of [\textit{X.-B. Lin}, Proc. R. Soc. Edinb., Ser. A 116, 295-325 (1990; Zbl 0714.34070)] and solutions of the adjoint variational equation, one gets a bifurcation function for periodic orbits, whose periods are asymptotic to infinity on ...
Ashwin, Peter, Mei, Zhen
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Homoclinic Orbits for Second-Order Hamiltonian Systems with Some Twist Condition
Abstract and Applied Analysis, 2012 We study the existence and multiplicity of homoclinic orbits for second-order Hamiltonian systems q¨−L(t)q+∇qW(t,q)=0, where L(t) is unnecessarily positive definite for all t∈ℝ, and ∇qW(t,q) is of at most linear growth and satisfies some twist condition ...
Qi Wang, Qingye Zhang
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BERNULLI DIFFERENTIAL EQUATION AND CHAOS
Vìsnik Dnìpropetrovsʹkogo Unìversitetu: Serìâ Modelûvannâ, 2013 Existence conditions of homoclinic orbits for some systems of ordinary quadratic differential equations with singular linear part are founded. A realization of these conditions guarantees the existence of chaotic attractors at 3-D autonomous quadratic ...
V. Ye. Belozerov
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Bifurcations of cubic homoclinic tangencies in two-dimensional symplectic maps
, 2017 We study bifurcations of cubic homoclinic tangencies in two-dimensional symplectic maps. We distinguish two types of cubic homoclinic tangencies, and each type gives different first return maps derived to diverse conservative cubic H\'enon maps with ...
Gonchenko, Marina +2 more
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Numerical Algorithms for Homoclinic Orbits
, 2009 Dynamical systems occur in many areas of science, especially fluid dynamics. One is often interested in examining the structural changes in dynamical systems, and these are often related to the appearance or disappearance of solution trajectories connecting one or more stationary points.
Girdlestone, Stephen +1 more
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