A Strange Attractor with Large Entropy in the Unfolding of a Low Resonant degenerate homoclinic Orbit
نویسندگان
چکیده
The unfolding of a vector field exhibiting a degenerate homoclinic orbit of inclination-flip type is studied. The linear part of the unperturbed system possesses a resonance but the coefficient of the corresponding monomial vanishes. We show that for an open set in the parameter space, the system possesses a suspended cubic Hénon-like map. As a consequence, strange attractors with entropy close to log 3 persist in a positive Lebesgue measure set.
منابع مشابه
A cubic Hénon-like map in the unfolding of degenerate homoclinic orbit with resonance
In this Note, we study the unfolding of a vector field that possesses a degenerate homoclinic (of inclination-flip type) to a hyperbolic equilibrium point where its linear part possesses a resonance. For the unperturbed system, the resonant term associated with the resonance vanishes. After suitable rescaling, the Poincaré return map is a cubic Hénon-like map. We deduce the existence of a stran...
متن کاملA strange attractor in the unfolding of an orbit- ̄ip homoclinic orbit
An orbit̄ip homoclinic orbit ¡ of a vector ®eld de®ned on R is a homoclinic orbit to an equilibrium point for which the one-dimensional unstable manifold of the equilibrium point is connected to the one-dimensional strong stable manifold. In this paper, we show that in a generic unfolding of such a homoclinic orbit, there exists a positive Lebesgue measure set in the parameter space for which th...
متن کاملPeriodic attractors, strange attractors and hyperbolic dynamics near homoclinic orbits to saddle-focus equilibria
We discuss dynamics near homoclinic orbits to saddle-focus equilibria in threedimensional vector fields. The existence of periodic and strange attractors is investigated not in unfoldings, but in families for which each member has a homoclinic orbit. We consider how often, in the sense of measure, periodic and strange attractors occur in such families. We also discuss the fate of typical orbits...
متن کاملResonant Homoclinic Bifurcations with Orbit Flips and Inclination Flips
Homoclinic bifurcation with one orbit flip, two inclination flips and resonance in the tangent directions of homoclinic orbit is considered. By studying the associated successor functions constructed from a local active coordinate system, we prove the existence of double 1-periodic orbit, 1-homoclinic orbit, and also some coexistence conditions of 1-periodic orbit and 1-homoclinic orbit.
متن کاملClassification of strange attractors by integers.
We show how to characterize a strange attractor by a set of integers. These are extracted from the chaotic time-series data by first reconstructing the low-period orbits and then determining the template, or knot holder, which supports all periodic orbits embedded in the strange attractor, and the strange attractor itself. The template is identified by a set of integers which therefore characte...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
- I. J. Bifurcation and Chaos
دوره 16 شماره
صفحات -
تاریخ انتشار 2006