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We study intermittent maps from the point of view of metastability. Small neighbourhoods of an intermittent fixed point and their complements form pairs of almost-invariant sets.
The goal of this paper is to provide a link between the parameter spaces of two families of one-dimensional dynamical systems, and to shed some light onto some sets of numbers which arise as “exceptio...
Our main result states that every fixed-point free continuous self-map of ${\mathbb R}^{n}$ is colorable. This result can be re-formulated as follows: A continuous map $f: {\mathbb R}^{n}\to {\mathbb...
We prove a general comparison result for homotopic finite $p$-energy $C^{1}$ $p$-harmonic maps $u,v:M\to N$ between Riemannian manifolds, assuming that $M$ is $p$-parabolic and $N$ is complete and non...
Homotopy Normal Maps     Homotopy Normal Maps  math  Algebraic Topology       2010/11/24
Normal maps between discrete groups $N\rightarrow G$ were characterized[FS] as those which induce a compatible topological group structure on the homotopy quotient $EN\times_N G$. Here we deal with to...
Let X be a separable Banach space which admits a separating polynomial; in particular X a separable Hilbert space. Let $f:X \rightarrow R$ be bounded, Lipschitz, and $C^1$ with uniformly continuous d...
We consider discrete metric spaces and we look for non-constant contractions. We introduce the notion of contractive map and we characterize the spaces with non-constant contractive maps. We provide s...
Let $C^*(E)$ be the graph $C^*$-algebra associated to a graph E and let J be a gauge invariant ideal in $C^*(E)$. We compute the cyclic six-term exact sequence in $K$-theory of the associated extensio...
The operator-sum decomposition (OS) of a mapping from one density matrix to another has many applications in quantum information science. To this mapping there corresponds an affine map which provides...
What input signals will lead to synchrony vs. desynchrony in a group of biological oscillators? This question connects with both classical dynamical sys- tems analyses of entrainment and phase locking...
Alternating patterns of small and large amplitude oscillations occur in a wide variety of physical, chemical, biological and engineering systems. These mixed-mode oscillations (MMOs) are often found i...
Closed form expressions in terms of multi-sums of products have been given for integrals of sine-Gordon, modi?ed Korteweg-de Vries and potential Korteweg-de Vries maps obtained as (p,-1)-traveling wav...
Dynamical A and B maps have been employed extensively by Sudarshan and co-workers to investigate open system evolution of quantum systems. A canonical structure of the A-map is introduced here. It is ...
A unicellular map is the embedding of a connected graph in a surface in such a way that the complement of the graph is simply connected. In a famous article, Harer and Zagier established a formula fo...
We study the global dynamics of integrate and fire neural networks composed of an arbitrary number of identical neurons interacting by inhibition and excitation. We prove that if the interactions are...

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