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Polynomial Estimates and Discrete Saddle-Node Homoclinic Orbits

✍ Scribed by Thorsten Hüls; Yongkui Zou

Publisher
Elsevier Science
Year
2001
Tongue
English
Weight
97 KB
Volume
256
Category
Article
ISSN
0022-247X

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✦ Synopsis

We derive polynomial rates of convergence for orbits of maps that converge to an equilibrium via the center manifold. Similar estimates are obtained for the variational equation along these orbits. We show how these results apply to the analysis of discrete saddle-node homoclinics.

📜 SIMILAR VOLUMES

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We consider 4-dimensional, real, analytic Hamiltonian systems with a saddle center equilibrium (related to a pair of real and a pair of imaginary eigenvalues) and a homoclinic orbit to it. We find conditions for the existence of transversal homoclinic orbits to periodic orbits of long period in ever

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Perturbed discrete systems like x n+1 = f x n + µg x n µ , x n ∈ N , n ∈ , when the associated unperturbed map (µ = 0) is not invertible and has a critical orbit γ n homoclinic to a hyperbolic fixed point p are studied. By critical we mean that the f γ n are invertible for any integer n = 0 but f γ