Related papers: A 1-dimensional Peano continuum which is not an IF…
We construct an example of planar Anosov diffeomorphisms without fixed points which is not topologically conjugate to a translation.
We define the Peano dimension for groups arising as fundamental groups, which generalizes the classical definition of geometric dimension of finitely presented groups. We conjecture that the Peano dimension of the fundamental group of a…
Our first main result is a construction of a simple formal normal form for holomorphic diffeomorphisms in C^n whose differentials have one-dimensional family of resonances in the first m eigenvalues, m <= n (but more resonances are allowed…
We construct a diffeomorphism of the two-dimensional torus which is isotopic to the identity and whose rotation set is not a polygon.
An infinite iterated function system (IIFS) is a countable collection of contraction maps on a compact metric space. In this paper we study the conditions under which the attractor of a such system admits a parameterization by a continuous…
This paper examines thresholds for certain properties of the attractor of a general one-parameter affine family of iterated functions systems. As the parameter increases, the iterated function system becomes less contractive, and the…
We define two non-metrizable compact spaces and show that they are attractors of iterated function systems. Both of them, the split square and the split carpet, are constructed using the product of split intervals.
The present paper is devoted to a study of orientation-preserving homeomorphisms on three-dimensional manifolds with a non-wandering set consisting of a finite number of surface attractors and repellers. The main results of the paper relate…
We construct an example of a closed manifold with a nonflat reducible locally metric connection such that it preserves a conformal structure and such that it is not the Levi-Civita connection of a Riemannian metric.
In this paper, we will show that a periodic nonlinear, time-varying dissipative system that is defined on a genus-p surface contains one or more invariant sets which act as attractors. Moreover, we shall generalize a result in [Martins,…
An embedding of chaotic data into a suitable phase space creates a diffeomorphism of the original attractor with the reconstructed attractor. Although diffeomorphic, the original and reconstructed attractors may not be topologically…
Iterated function systems (IFSs) and their attractors have been central to the theory of fractal geometry almost from its inception. And contractivity of the functions in the IFS has been central to the theory of iterated functions systems.…
The space of chains on a compact connected space encodes all the different ways of continuously growing out of a point until exhausting the space. A chain is \emph{generic} if its orbit under the action of the underlying homeomorphism group…
In this paper, we define inhomogeneous Graph-Directed (GD) separation conditions for a given inhomogeneous GD Iterated Function Systems (IFS), and estimate the upper box dimension of attractors by the dimension of the condensation set and…
This is the first article in a two-part series containing some results on dimension estimates for $C^1$ iterated function systems and repellers. In this part, we prove that the upper box-counting dimension of the attractor of any $C^1$…
On every compact 3-manifold, we build a non-empty open set $\cU$ of $\Diff^1(M)$ such that, for every $r\geq 1$, every $C^r$-generic diffeomorphism $f\in\cU\cap \Diff^r(M)$ has no topological attractors. On higher dimensional manifolds, one…
We show that the Cantorvals connected with the geometric Cantor sets are not achievement sets of any series. However many of them are attractors of IFS consisting of affine functions.
We present new examples of open sets of diffeomorphisms such that a generic diffeomorphisms in those sets have no dynamically indecomposable attractors in the topological sense and have infinitely many chain-recurrence classes. We show that…
We prove that given any closed $n$-manifold $M^n$, $n\geq 4$, there is an A-flow $f^t$ on $M^n$ such that the non-wandering set $NW(f^t)$ consists of 2-dimensional expanding attractor (the both, orientable and non-orientable) and trivial…
We deal with topological spaces homeomorphic to their respective squares. Primarily, we investigate the existence of large families of such spaces in some subclasses of compact metrizable spaces. As our main result we show that there is a…