Related papers: The Conley index for piecewise continuous maps
In this paper the concept of a partial cone metric space is investigated, some continuity type theorems, and fixed point theorems of contractive mappings in this generalized setting are proved as well as some theorems related to topological…
In this paper, we apply Conley index theory in a covering space of an invariant set $S$, possibly not isolated, in order to describe the dynamics in $S$. More specifically, we consider the action of the covering translation group in order…
A time-varying empirical spectral process indexed by classes of functions is defined for locally stationary time series. We derive weak convergence in a function space, and prove a maximal exponential inequality and a…
Numerical simulations of coupled map lattices (CMLs) and other complex model systems show an enormous phenomenological variety that is difficult to classify and understand. It is therefore desirable to establish analytical tools for…
We introduce the notion of one-sided mapping cones of positive linear maps between matrix algebras. These are convex cones of maps that are invariant under compositions by completely positive maps from either the left or right side. The…
In this paper, we establish a common fixed point theorem for two pairs of occasionally weakly compatible single and set-valued maps satisfying a strict contractive condition in a metric space. Our result extends many results existing in the…
We consider perturbations of interval maps with indifferent fixed points, which we refer to as wobbly interval intermittent maps, for which stable laws for general H\"older observables fail. We obtain limit laws for such maps and H\"older…
Maps $f,g\colon I\to I$ are called strongly commuting if $f\circ g^{-1}=g^{-1}\circ f$. We show that strongly commuting, piecewise monotone maps $f,g$ can be decomposed into a finite number of invariant intervals (or period 2 intervals) on…
The central purpose of this article is to establish new inverse and implicit function theorems for differentiable maps with isolated critical points. One of the key ingredients is a discovery of the fact that differentiable maps with…
Recent work by Prodan and the second author showed that weak invariants of topological insulators can be described using Kasparov's $KK$-theory. In this note, a complementary description using semifinite index theory is given. This provides…
We already know a great deal about dynamical systems with uniqueness in forward time. Indeed, flows, semiflows, and maps (both invertible and not) have been studied at length. A view that has proven particularly fruitful is topological:…
Let $g:\, [0, 1]\rightarrow [0, 1]$ be piecewise linear unimodal map. We say that $g$ has non-trivial piecewise linear commutator, if there is a continuous piecewise linear $\psi:\, [0, 1]\rightarrow [0, 1]$ such that $g\circ \psi =…
We study properties of strongly separately continuous mappings defined on subsets of products of topological spaces equipped with the topology of pointwise convergence. In particular, we give a necessary and sufficient condition for a…
We define a notion of stable and measurable map between cones endowed with measurability tests and show that it forms a cpo-enriched cartesian closed category. This category gives a denotational model of an extension of PCF supporting the…
We characterize the equivalence and the weak equivalence of Cayley graphs for a finite group $\C{A}$. Using these characterizations, we find enumeration formulae of the equivalence classes and weak equivalence classes of Cayley graphs. As…
In this paper we study the existence and uniqueness of fixed points of a class of mappings defined on complete, (sequentially compact) cone metric spaces, without continuity conditions and depending on another function.
Jacobi-type algorithms for simultaneous approximate diagonalization of real (or complex) symmetric tensors have been widely used in independent component analysis (ICA) because of their good performance. One natural way of choosing the…
Let X and Y be finite dimensional normed spaces, F(X,Y) a collection of all mappings from X into Y. A mapping $P\in F(X,Y)$ is said to be piecewise affine if there exists a finite family of convex polyhedral subsets covering X and such that…
The clustering coefficient of a vertex in a graph is the proportion of neighbours of the vertex that are adjacent. The minimum clustering coefficient of a graph is the smallest clustering coefficient taken over all vertices. A complete…
Firstly, we wish to motivate that Conley pairs, realized via Salamon's definition [17], are rather useful building blocks in geometry: Initially we met Conley pairs in an attempt to construct Morse filtrations of free loop spaces [21]. From…