By a dynamical system we mean the action of the semigroup on a metrizable topological space induced by a continuous selfmap . Let denote the set of all compatible metrics on the space . Our main objective is to show that a selfmap of a compact space is a Banach contraction relative to some if and only if there exists some which, regarded as a -cocycle of the system , is a coboundary.
In this paper piecewise monotonic maps are considered. Let be a finite union of open intervals, and consider the set of all points whose orbits omit . The influence of small perturbations of the endpoints of the intervals in on the dynamical system is investigated. The decomposition of the nonwandering set into maximal topologically transitive subsets behaves very unstably. Nonetheless, it is shown that a maximal topologically transitive subset cannot be completely destroyed by arbitrary...
We give a brief introduction to the Bernoulli shift map as a basic chaotic dynamical system. We give several examples where the iterates of a~mapping can be understood using the Bernoulli shift. Namely, the iteration of real interval maps and iteration of quadratic functions in the complex plain.
In questo lavoro vengono generalizzati i risultati relativi al problema del rimbalzo unidimensionale studiato in [5]. Precisamente si considera un punto mobile su una varietà Riemanniana -dimensionale, soggetto all’azione di un potenziale variabile nel tempo e vincolato a restare in una parte di avente un bordo di classe contro cui il punto «rimbalza»....
If φ is a Pisot substitution of degree d, then the inflation and substitution homeomorphism Φ on the tiling space factors via geometric realization onto a d-dimensional solenoid. Under this realization, the collection of Φ-periodic asymptotic tilings corresponds to a finite set that projects onto the branch locus in a d-torus. We prove that if two such tiling spaces are homeomorphic, then the resulting branch loci are the same up to the action of certain affine maps on the torus.
Answering a question of Smale, we prove that the space of C 1 diffeomorphisms of a compact manifold contains a residual subset of diffeomorphisms whose centralizers are trivial.
We prove that the algebraic multiplicity of a holomorphic vector field at an isolated singularity is invariant by equivalences.
For a self-map of a compactum we give a necessary and sufficient condition for the chain recurrent set to be precisely the set of periodic points.