Let f be a continuous map of an interval into itself having periodic points of period 2n for all n ≥ 0 and no other periods. It is shown that every neighborhood of f contains a map g such that the set of periods of the periodic points of g is finite. This answers a question posed by L. S. Block and W. A.

I t is easy to see that for every point (y, N) in WXI there is a solution (n) of (1) that satisfies <1>(N) =y. This solution is defined and unique on some set N^nKN*» where N<» is maximal. (That is, either iV» = °o or ^ i V ^ — l) (£W.) The solution may or may not be continuable for nƒ> rc)> 0^w<iV o o(^ , / ) , be the soluti...

The recent paper [1] enlightens the interest of a class of switching rules with nice properties, called eventually periodic: it is proven that a finite family F of linear vector fields of R d can be stabilized by means of eventually periodic switching rules, provided that it is asymptotically controllable and satisfies an additional finite time controllability condition. Unfortunately, simple e...

We show that, for monotone graph map f , all the ω-limit sets are finite whenever f has periodic point and for monotone dendrite map, any infinite ω-limit set does not contain periodic points. As a consequence, monotone graph and dendrite maps have no Li-Yorke pairs. However, we built a homeomorphism on a dendroid with a scrambled set having nonempty interior.

The nonlinear differential equation x" = f(t, x(t)), f being 22T-periodic in t, is considered for the existence of 27T-periodic solutions. The equation is reduced to an equivalent system of two Hammerstein equations. The case of nonlinear perturbation at resonance is also discussed.

Let f : M → M be a C-map on a smooth Riemannian manifold M and let Λ ⊂ M be a compact f -invariant locally maximal set. In this paper we obtain several results concerning the distribution of the periodic orbits of f |Λ. These results are non-invertible and, in particular, non-uniformly hyperbolic versions of well-known results by Bowen, Ruelle, and others in the case of hyperbolic diffeomorphis...

Let (X, f) be a topological dynamical system. We say that it is partially periodic point free up to period n, if f does not have periodic points of periods smaller than n + 1. When X is a compact connected surface, a connected compact graph, or S ∨ S ∨ · · · ∨ S, we give conditions on X, so that there exist partially periodic point free maps up to period n. We also introduce the notion of a Lef...

The differential equation ẍ+γẋ+x = f(t) with f(t) positive, periodic and continuous is studied. After describing some physical applications of this equation, we construct a variety of invariant sets for it, thereby partitioning the phase plane into regions in which solutions grow without bound and also those in which bounded periodic solutions exist.

Although the spectrum of radially periodic images is often expressed in terms of finite or infinite series of Bessel functions, such expressions do not clearly reveal the exact impulsive structure of the spectrum. An alternative Fourier decomposition of radially periodic images, in terms of circular cosine functions, is presented, and its significant advantages are shown. It is shown that the F...

0. Introduction. The Fatou set of a holomorphic map f : P is the largest open subset of P on which iterates of f form a normal family. The complement of is called the Julia set when k = 1, and it is well known that the Julia set is the closure of the set of repelling periodic points. When k = 2, however, even product maps suffice to show that the structure of P2\ is more intricate. For instance...