Search results for "Limit set"
showing 10 items of 11 documents
Attractors for non-autonomous retarded lattice dynamical systems
2015
AbstractIn this paperwe study a non-autonomous lattice dynamical system with delay. Under rather general growth and dissipative conditions on the nonlinear term,we define a non-autonomous dynamical system and prove the existence of a pullback attractor for such system as well. Both multivalued and single-valued cases are considered.
ATTRACTORS FOR A LATTICE DYNAMICAL SYSTEM GENERATED BY NON-NEWTONIAN FLUIDS MODELING SUSPENSIONS
2010
In this paper we consider a lattice dynamical system generated by a parabolic equation modeling suspension flows. We prove the existence of a global compact connected attractor for this system and the upper semicontinuity of this attractor with respect to finite-dimensional approximations. Also, we obtain a sequence of approximating discrete dynamical systems by the implementation of the implicit Euler method, proving the existence and the upper semicontinuous convergence of their global attractors.
A note on correlation and local dimensions
2015
Abstract Under very mild assumptions, we give formulas for the correlation and local dimensions of measures on the limit set of a Moran construction by means of the data used to construct the set.
Description of the limit set of Henstock–Kurzweil integral sums of vector-valued functions
2015
Abstract Let f be a function defined on [ 0 , 1 ] and taking values in a Banach space X . We show that the limit set I HK ( f ) of Henstock–Kurzweil integral sums is non-empty and convex when the function f has an integrable majorant and X is separable. In the same setting we give a complete description of the limit set.
On a Planar Dynamical System Arising in the Network Control Theory
2016
We study the structure of attractors in the two-dimensional dynamical system that appears in the network control theory. We provide description of the attracting set and follow changes this set suffers under the changes of positive parameters µ and Θ.
Passive time-multiplexing super-resolved technique for axially moving targets
2013
In this paper we present a super-resolving approach for detecting an axially moving target that is based upon a time-multiplexing concept and that overcomes the diffraction limit set by the optics of an imaging camera by a priori knowledge of the high-resolution background in front of which the target is moving. As the movement trajectory is axial, the approach can be applied to targets that are approaching or moving away from the camera. By recording a set of low-resolution images at different target axial positions, the super-resolving algorithm weights each image by demultiplexing them using the high-resolution background image and provides a super-resolved image of the target. Theoretic…
Free vs. Locally Free Kleinian Groups
2015
Abstract We prove that Kleinian groups whose limit sets are Cantor sets of Hausdorff dimension < < 1 are free. On the other hand we construct for any ε > > 0 an example of a non-free purely hyperbolic Kleinian group whose limit set is a Cantor set of Hausdorff dimension < < 1 + + ε.
The Kuratowski convergence and connected components
2012
International audience; We investigate the Kuratowski convergence of the connected components of the sections of a definable set applying the result obtained to semialgebraic approximation of subanalytic sets. We are led to some considerations concerning the connectedness of the limit set in general. We discuss also the behaviour of the dimension of converging sections and prove some general facts about the Kuratowski convergence in tame geometry.
Surface homeomorphisms with zero dimensional singular set
1998
We prove that if f is an orientation-preserving homeomorphism of a closed orientable surface M whose singular set is totally disconnected, then f is topologically conjugate to a conformal transformation.
Some Applications of the Poincaré-Bendixson Theorem
2021
We consider a C 1 vector field X defined on an open subset U of the plane, with compact closure. If X has no singular points and if U is simply connected, a weak version of the Poincaré-Bendixson Theorem says that the limit sets of X in U are empty but that one can defined non empty extended limit sets contained into the boundary of U. We give an elementary proof of this result, independent of the classical Poincaré-Bendixson Theorem. A trapping triangle T based at p, for a C 1 vector field X defined on an open subset U of the plane, is a topological triangle with a corner at a point p located on the boundary ∂U and a good control of the tranversality of X along the sides. The principal app…