The search session has expired. Please query the service again.
The search session has expired. Please query the service again.
The search session has expired. Please query the service again.
The search session has expired. Please query the service again.
The search session has expired. Please query the service again.
The search session has expired. Please query the service again.
The search session has expired. Please query the service again.
The search session has expired. Please query the service again.
The search session has expired. Please query the service again.
We provide a topological proof that each orientation reversing homeomorphism of the 2-sphere which has a point of period k ≥ 3 also has a point of period 2. Moreover if such a k-periodic point can be chosen arbitrarily close to an isolated fixed point o then the same is true for the 2-periodic point. We also strengthen this result by proving that if an orientation reversing homeomorphism h of the sphere has no 2-periodic point then the complement of the fixed point set can be covered by invariant...
This is a study of the monotone (in parameter) behavior of the ratios of the consecutive intervals in the nested family of intervals delimited by the itinerary of a critical point. We consider a one-parameter power-law family of mappings of the form . Here we treat the dynamically simplest situation, before the critical point itself becomes strongly attracting; this corresponds to the kneading sequence RRR..., or-in the quadratic family-to the parameters c ∈ [-1,0] in the Mandelbrot set. We allow...
For continuous maps on the interval with finitely many monotonicity intervals, the kneading theory developed by Milnor and Thurston gives a symbolic description of the dynamics of a given map. This description is given in terms of the kneading invariants which essentially consists in the symbolic orbits of the turning points of the map under consideration. Moreover, this theory also describes a classification of all such maps through theses invariants. For continuous bimodal degree one circle maps,...
For a piecewise monotone map f on a compact interval I, we characterize the ω-limit sets that are bounded away from the post-critical points of f. If the pre-critical points of f are dense, for example when f is locally eventually onto, and Λ ⊂ I is closed, invariant and contains no post-critical point, then Λ is the ω-limit set of a point in I if and only if Λ is internally chain transitive in the sense of Hirsch, Smith and Zhao; the proof relies upon symbolic dynamics. By identifying points of...
We work within the one-parameter family of symmetric tent maps, where the slope is the parameter. Given two such tent maps , with periodic critical points, we show that the inverse limit spaces and are not homeomorphic when a ≠ b. To obtain our result, we define topological substructures of a composant, called “wrapping points” and “gaps”, and identify properties of these substructures preserved under a homeomorphism.
A class of functional equations with nonlinear iterates is discussed on the unit circle . By lifting maps on and maps on the torus to Euclidean spaces and extending their restrictions to a compact interval or cube, we prove existence, uniqueness and stability for their continuous solutions.
In the theory of autonomous perturbations of periodic solutions of ordinary differential equations the method of the Poincaré mapping has been widely used. For the analysis of properties of this mapping in the case of two-dimensional systems, a result first obtained probably by Diliberto in 1950 is sometimes used. In the paper, this result is (partially) extended to a certain class of autonomous ordinary differential equations of higher dimension.
Let f be a nonrenormalizable S-unimodal map. We prove that f is a Collet-Eckmann map if its dynamical zeta function looks like that of a uniformly hyperbolic map.
In a series of papers, Bandt and the author have given a symbolic and topological description of locally connected quadratic Julia sets by use of special closed equivalence relations on the circle called Julia equivalences. These equivalence relations reflect the landing behaviour of external rays in the case of local connectivity, and do not apply completely if a Julia set is connected but fails to be locally connected. However, rational external rays land also in the general case. The present...
We describe a technique that maps unranked trees to arbitrary hash
codes using a bottom-up deterministic tree automaton (DTA). In
contrast to other hashing techniques based on automata, our
procedure builds a pseudo-minimal DTA for this purpose. A
pseudo-minimal automaton may be larger than the minimal one
accepting the same language but, in turn, it contains proper
elements (states or transitions which are unique) for every input
accepted by the automaton. Therefore, pseudo-minimal DTA...
We prove that the standard action of the mapping class group of a surface of sufficiently large genus on the unit tangent bundle is not homotopic to any smooth action.
Currently displaying 1 –
20 of
42