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Glendinning, Paul; Sparrow, Colin

Local and global behavior near homoclinic orbits. (English) Zbl 0588.58041

J. Stat. Phys. 35, 645-696 (1984).
We study the local behavior of systems near homoclinic orbits to stationary points of saddle-focus type. We explicitly describe how a periodic orbit approaches homoclinicity and, with the help of numerical examples, discuss how these results relate to global patterns of bifurcations.

Cited in 141 Documents

MSC:

37D45 Strange attractors, chaotic dynamics of systems with hyperbolic behavior
37G99 Local and nonlocal bifurcation theory for dynamical systems

Keywords:

chaos; period-doubling; homoclinic orbits; bifurcations
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\textit{P. Glendinning} and \textit{C. Sparrow}, J. Stat. Phys. 35, 645--696 (1984; Zbl 0588.58041)
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References:

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