A Numerical Bifurcation Function for Homoclinic Orbits
نویسندگان
چکیده
منابع مشابه
A Numerical Bifurcation Function for Homoclinic Orbits
We present a numerical method to locate periodic orbits near homoclinic orbits. Using a method of X.-B. Lin and solutions of the adjoint variational equation, we get a bifurcation function for periodic orbits whose period is asymptotic to innnity on approaching a homoclinic orbit. As a bonus, a linear predictor for continuation of the homoclinic orbit is easily available. Numerical approximatio...
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We prove the existence of symmetric homoclinic orbits to a saddle-focus symmetric periodic orbit that appears in a generic family of reversible three degrees of freedom Hamiltonian system due to periodic Hamiltonian Hopf bifurcation, if some coefficient A of the normal form of the fourth order is positive. If this coefficient is negative, then for the opposite side of the bifurcation parameter ...
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We study a generic piecewise monotone map f : [0, 1] → [0, 1] with a particular type of entropy-carrying set X. We show under certain conditions that maps sufficiently C-close to f with more topological entropy have entropy-carrying sets containing X. New homoclinic orbits are created to every periodic point of X. 2000 Mathematics Subject Classification (MSC2000). 37E05, 37B40, 37Gxx
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Transversal homoclinic orbits of maps are known to generate shift dynamics on a set with Cantor like structure. In this paper a numerical method is developed for computation of the corresponding homoclinic orbits. They are approximated by nite orbit segments subject to asymptotic boundary conditions. We provide a detailed error analysis including a shadowing type result by which one can infer t...
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ژورنال
عنوان ژورنال: SIAM Journal on Numerical Analysis
سال: 1998
ISSN: 0036-1429,1095-7170
DOI: 10.1137/s0036142996298168