Über einen Satz von SEVERI über unirationale Systeme auf algebraischen Mannigfaltigkeiten
Über die Verallgemeinerung eines Satzes von Bertini auf eindimensionale unirationale Scharen.
Das Typenproblem bei formal-biholomorphen Abbildungen mit anziehendem Fixpunkt.
Normalformen biholomorpher Abbildungen mit anziehendem Fixpunkt.
Biholomorphe Abbildungen mit anziehendem Fixpunkt und analytische Differentialgleichungssysteme in Nähe einer Gleichgewichtslage.
Über unirationale Scharen auf algebraischen Mannigfaltigkeiten
Zur Majorantenmethode im Normalformenproblem für analytische Differentialgleichungssysteme.
Über die Funktionalgleichung N...T = T...M für formale Potenzreihen. (Short Communication).
Linearization of formally biholomorphic mappings and iteration problems (Short Communication).
Über die Funktionengleichung N?T = T?M für formale Potenzreihen.
The continuous solutions of a generalized Dhombres functional equation
We consider the functional equation where is a given increasing homeomorphism of an open interval and is an unknown continuous function. In a series of papers by P. Kahlig and J. Smítal it was proved that the range of any non-constant solution is an interval whose end-points are fixed under and which contains in its interior no fixed point except for . They also provide a characterization of the class of monotone solutions and prove a necessary and sufficient condition for any solution...
The converse problem for a generalized Dhombres functional equation
We consider the functional equation where is a given homeomorphism of an open interval and is an unknown continuous function. A characterization of the class of continuous solutions is given in a series of papers by Kahlig and Smítal 1998–2002, and in a recent paper by Reich et al. 2004, in the case when is increasing. In the present paper we solve the converse problem, for which continuous maps , where is an interval, there is an increasing homeomorphism of such that . We...
Forewords : European Conference on Iteration Theory - ECIT 2010
Some remarks on the general theorem of the existence of iterative roots of homeomorphisms with a rational rotation number
We show that the theorem proved in [8] generalises the previous results concerning orientation-preserving iterative roots of homeomorphisms of the circle with a rational rotation number (see [2], [6], [10] and [7]).
Invariant graphs of functions for the mean-type mappings
Let
Gibbs-Markov-Young structures, ,
We discuss the geometric structures defined by Young in [9, 10], which are used to prove the existence of an ergodic absolutely continuous invariant probability measure and to study the decay of correlations in expanding or hyperbolic systems on large parts.
Coexisting cycles in a class of 3-D discrete maps
In this paper we consider the class of three-dimensional discrete maps () = [(), (), ()], where : ℝ → ℝ is an endomorphism. We show that all the cycles of the 3-D map can be obtained by those of (), as well as their local bifurcations. In particular we obtain that any local bifurcation is of co-dimension 3, that is three eigenvalues cross simultaneously the unit circle. As the map exhibits coexistence of cycles when ...
Some aspects of the local theory of generalized Dhombres functional equations in the complex domain
We study the generalized Dhombres functional equation (()) = (()) in the complex domain. The function is given and we are looking for solutions with (0) = and is a primitive root of unity of order ≥ 2. All formal solutions for this case are described in this work, for the situation where can be transformed into a function which is linearizable and local analytic in a neighbourhood of zero...
Example of the Smooth Skew Product in the Plane with the One-dimensional Ramified Continuum as the Global Attractor
The example is constructed of the -smooth skew product of interval maps possessing the one-dimensional ramified continuum (containing no arcs homeomorphic to the circle) with an infinite set of ramification points as the global attractor.
Breaking the continuity of a piecewise linear map
Knowledge about the behavior of discontinuous piecewise-linear maps is important for a wide range of applications. An efficient way to investigate the bifurcation structure in 2D parameter spaces of such maps is to detect specific codimension-2 bifurcation points, called organizing centers, and to describe the bifurcation structure in their neighborhood. In this work, we present the organizing centers in the 1D discontinuous piecewise-linear map...
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