Results 81 to 90 of about 2,056 (109)

Saddle-node bifurcation of viscous profiles.

Physica D, 2012
Achleitner F, Szmolyan P.
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On the Structure of Orbits from a Neighborhood of a Transversal Homoclinic Orbit to a Nonhyperbolic Fixed Point

Regular and Chaotic Dynamics
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Gonchenko, Sergey V., Gordeeva, Ol'ga V.
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The density of the transversal homoclinic points in the Henon-like strange attractors

Chaos, Solitons & Fractals, 2002
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Cao, Yongluo, Kiriki, Shin
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The transversal homoclinic point of a saddle-node implies horseshoe

Science in China Series A: Mathematics, 1999
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Transversal homoclinic points and hyperbolic sets for non-autonomous maps II

ZAMP Zeitschrift f�r angewandte Mathematik und Physik, 1988
The paper continues the study performed by the author in [ibid. 39, No. 4, 518--549 (1988; Zbl 0672.58034)] where the concept of hyperbolic sets and transversal homoclinic points to non-autonomous systems has been generalized. The main result of this work is to exhibit conditions which imply the existence of transverse homoclinic orbits for such ...
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Chaotic behaviour near non-transversal homoclinic points with quadratic tangency

Journal of Difference Equations and Applications, 2006
We consider a one-parameter family of discrete dynamical systems which has, for a critical value of the parameter, a homoclinic point with a quadratic tangency. We use Lin's method to prove the existence of shift dynamics near this homoclinic orbit.
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Transversal Homoclinic Points of Diffeomorphisms and Hyperbolic Sets

2000
Up till now our only examples of hyperbolic sets have been hyperbolic fixed points and periodic orbits. In this chapter we give an example of a hyperbolic set which is infinite. Moreover, even though the set consists of only two distinct orbits, we shall show in Chapter 5 that in its neighbourhood the diffeomorphism has chaotic dynamics.
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Exponential Dichotomies, the Shadowing Lemma and Transversal Homoclinic Points

1988
Smale [12,13] studied diffeomorphisms with transversal homoclinic points and showed that the dynamics are chaotic in the neighbourhood of the orbit of such a point, in the sense that there is a compact invariant set on which the action of some iterate of the diffeomorphism is topologically conjugate to the action of the Bernoulli shift.
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Symbolic Dynamics Near a Transversal Homoclinic Point of a Diffeomorphism

2000
In Chapter 3 we showed that the set consisting of a hyperbolic fixed point of a diffeomorphism and an associated transversal homoclinic orbit is hyperbolic. In this chapter we use symbolic dynamics to describe all the orbits in a neighbourhood of this set. In particular, we shall show that the dynamics in such a neighbourhood is chaotic.
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Transversal Homoclinic Orbits near Elliptic Fixed Points of Area-preserving Diffeomorphisms of the Plane

1993
Extending a result due to E. Zehnder [27], we prove that generically, an area-preserving analytic diffeomorphism of the plane has transversal homoclinic orbits and nondegenerate Mather sets in every neighborhood of a stable elliptic fixed point. “Generically” refers to a topology defined by means of the Taylor coefficients of the mapping at the fixed ...
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