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Distribution of Maps with Transversal Homoclinic Orbits in a Continuous Map Space
Abstract and Applied Analysis, 2011 This paper is concerned with distribution of maps with transversal homoclinic orbits in a continuous map space, which consists of continuous maps defined in a closed and bounded set of a Banach space.
Qiuju Xing, Yuming Shi
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Homoclinic orbits for periodic second order Hamiltonian systems with superlinear terms
Electronic Journal of Qualitative Theory of Differential Equations, 2022 We obtain the existence of nontrivial homoclinic orbits for nonautonomous second order Hamiltonian systems by using critical point theory under some different superlinear conditions from those previously used in Hamiltonian systems.
Haiyan Lv, Guanwei Chen
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Bifurcations of Orbit and Inclination Flips Heteroclinic Loop with Nonhyperbolic Equilibria
The Scientific World Journal, 2014 The bifurcations of heteroclinic loop with one nonhyperbolic equilibrium and one hyperbolic saddle are considered, where the nonhyperbolic equilibrium is supposed to undergo a transcritical bifurcation; moreover, the heteroclinic loop has an orbit flip ...
Fengjie Geng, Junfang Zhao
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Homoclinic orbits of sub-linear Hamiltonian systems with perturbed terms
Boundary Value Problems, 2021 By using variational methods, we obtain the existence of homoclinic orbits for perturbed Hamiltonian systems with sub-linear terms. To the best of our knowledge, there is no published result focusing on the perturbed and sub-linear Hamiltonian systems.
Haiyan Lv, Guanwei Chen
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Abstract and Applied Analysis, 2013 We study a class of nonperiodic damped vibration systems with asymptotically quadratic terms at infinity. We obtain infinitely many nontrivial homoclinic orbits by a variant fountain theorem developed recently by Zou.
Guanwei Chen
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Solitary Waves and Homoclinic Orbits [PDF]
Annual Review of Fluid Mechanics, 1995 The notion that fluid motion often organizes itself into coherent structures has increasingly permeated modern fluid dynamics. Such localized objects appear in laminar flows and persist in turbulent states; from the water on windows on rainy days, to the circulations in planetary atmospheres. This review concerns solitary waves in fluids.
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Homoclinic Orbits around Spinning Black Holes I: Exact Solution for the Kerr Separatrix
, 2008 Under the dissipative effects of gravitational radiation, black hole binaries will transition from an inspiral to a plunge. The separatrix between bound and plunging orbits features prominently in the transition.
G. Perez-Giz +7 more
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, 2017 Floer theory was originally devised to estimate the number of 1-periodic orbits of Hamiltonian systems. In earlier works, we constructed Floer homology for homoclinic orbits on two dimensional manifolds using combinatorial techniques.
Hohloch, Sonja
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Journal of Biological Dynamics, 2020 In this paper, Melnikov analysis of chaos in a simple SIR model with periodically or stochastically modulated nonlinear incidence rate and the effect of periodic and bounded noise on the chaotic motion of SIR model possessing homoclinic orbits are ...
Yanxiang Shi
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Homoclinic Orbits for a Class of Nonperiodic Hamiltonian Systems
Abstract and Applied Analysis, 2012 We study the following nonperiodic Hamiltonian system ż=JHz(t,z), where H∈C1(R×R2N,R) is the form H(t,z)=(1/2)B(t)z⋅z+R(t,z). We introduce a new assumption on B(t) and prove that the corresponding Hamiltonian operator has only point spectrum.
Wenping Qin, Jian Zhang, Fukun Zhao
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