1 - 10 of 11 articles
The process of random walk can be demonstrated to occur in the three-body problem. This is shown to be the case for a family of horseshoe orbits. This offers a possible alternate approach to studying special motions of this problem and other problems in celestial mechanics.
Systems of material points interacting both with one another and with an external field are considered in Euclidean space. For the case of arbitrary binary interaction depending solely on the mutual distance between the bodies, new integrals are found, which form a Galilean momentum vector. A...
We show that a focusing component Γ of the boundary of a billiard table is absolutely focusing iff a sequence of convergents of a continued fraction corresponding to any series of consecutive reflections off Γ is monotonic. That is, if Γ is absolutely focusing this implies monotonicity of...
We consider nearly-integrable systems under a relatively small dissipation. In particular we investigate two specific models: the discrete dissipative standard map and the continuous dissipative spin-orbit model. With reference to such samples, we review some analytical and numerical results...
We study both theoretically and numerically the Lyapunov families which bifurcate in the vertical direction from a horizontal relative equilibrium in ℝ3. As explained in , very symmetric relative equilibria thus give rise to some recently studied classes of periodic solutions. We discuss the...
We study bifurcations of two-dimensional symplectic maps with quadratic homoclinic tangencies and prove results on the existence of cascade of elliptic periodic points for one and two parameter general unfoldings.
We study dynamics and bifurcations of three-dimensional diffeomorphisms with nontransverse heteroclinic cycles. We show that bifurcations under consideration lead to the birth of wild-hyperbolic Lorenz attractors. These attractors can be viewed as periodically perturbed classical Lorenz...
For a 2 d.o.f. Hamiltonian system we prove the Lyapunov stability of its equilibrium with two double pure imaginary eigenvalues and non-semisimple Jordan form for the linearization matrix, when some coefficient in the 4th order normal form is positive (the equilibrium is known to be unstable, if...
Read and print from thousands of top scholarly journals.
Already have an account? Log in
Bookmark this article. You can see your Bookmarks on your DeepDyve Library.
To save an article, log in first, or sign up for a DeepDyve account if you don’t already have one.
Sign Up Log In
To subscribe to email alerts, please log in first, or sign up for a DeepDyve account if you don’t already have one.
To get new article updates from a journal on your personalized homepage, please log in first, or sign up for a DeepDyve account if you don’t already have one.