Homoclinic orbits of invertible maps
نویسندگان
چکیده
In this paper, we present a systematic method for finding all homoclinic orbits of invertible maps in any finite dimension. One advantage of this method is that it can also be used to order and classify all the homoclinic orbits, using symbolic dynamics, if a certain criterion is satisfied. We also present a more direct scheme, which quickly locates homoclinic orbits without, however, being able to order and classify them. Our work represents an extension of a method introduced in an earlier paper, with which one could only find homoclinic orbits possessing a certain symmetry. Thus, asymmetric homoclinic orbits can now be as easily computed. One application of our results is the explicit construction of breather (and multibreather) solutions of a class of one-dimensional nonlinear lattices. Mathematics Subject Classification: 37C29, 37M99
منابع مشابه
The Numerical Computation of Homoclinic Orbits for Maps
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...
متن کاملN ov 2 00 3 Forcing relations for homoclinic and periodic orbits of the Smale horseshoe map ∗
An important problem in the dynamics of surface homeomorphisms is determining the forcing relation between orbits. The forcing relation between periodic orbits can be computed using standard algorithms, though this does not give much information on the structure of the forcing relation. Here we consider forcing relations between homoclinic orbits, and their relationships with periodic orbits. W...
متن کاملHomoclinic tangles for noninvertible maps
Not all naturally occurring iterated systems have the property that time is reversible. In which case, the dynamics must be modelled by a noninvertible map rather than by a di eomorphism. While one-dimensional theory describes dynamics of noninvertible maps, higher-dimensional theory has focussed on di eomorphisms, though there are many higher-dimensional examples of natural systems modelled by...
متن کاملExistence of Infinitely Many Elliptic Periodic Orbits in Four-Dimensional Symplectic Maps with a Homoclinic Tangency
We study the problem of coexistence of a countable number of periodic orbits of different topological types (saddles, saddle–centers, and elliptic) in the case of four-dimensional symplectic diffeomorphisms with a homoclinic trajectory to a saddle–focus fixed point.
متن کاملOn bifurcations of area-preserving and non-orientable maps with quadratic homoclinic tangencies
We study bifurcations of non-orientable area-preserving maps with quadratic homoclinic tangencies. We study the case when the maps are given on non-orientable two-dimensional surfaces. We consider one and two parameter general unfoldings and establish results related to the emergence of elliptic periodic orbits.
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:
دوره شماره
صفحات -
تاریخ انتشار 2002