Connected components of attractors and other stable sets.
Construction de flots de Smale en dimension 3
Construction of a smooth Lyapunov function for an asymptotically stable set
Construction of attractors and filtrations
This paper is a study of the global structure of the attractors of a dynamical system. The dynamical system is associated with an oriented graph called a Symbolic Image of the system. The symbolic image can be considered as a finite discrete approximation of the dynamical system flow. Investigation of the symbolic image provides an opportunity to localize the attractors of the system and to estimate their domains of attraction. A special sequence of symbolic images is considered in order to obtain...
Construction of entire solutions for semilinear parabolic equations.
Construction of invariant sets for Anosov diffeomorphisms and hyperbolic attractors
Continuity of attractors
Continuous and inverse shadowing for flows.
Continuous dependence of attractors on the shape of domain
Continuum-wise expansive diffeomorphisms.
In this paper, we show that the C1 interior of the set of all continuum-wise expansive diffeomorphisms of a closed manifold coincides with the C1 interior of the set of all expansive diffeomorphisms. And the C1 interior of the set of all continuum-wise fully expansive diffeomorphisms on a surface is investigated. Furthermore, we have necessary and sufficient conditions for a diffeomorphism belonging to these open sets to be Anosov.
Contracting singular cycles
Contractions of Nadler type on partial tvs-cone metric spaces
This paper introduces partial tvs-cone metric spaces as a common generalization of both tvs-cone metric spaces and partial metric spaces, and gives a new fixed point theorem for contractions of Nadler type on partial tvs-cone metric spaces. As corollaries, we obtain the main results of S. B. Nadler (1969), D. Wardowski (2011), S. Radenović et al. (2011) and H. Aydi et al. (2012) are deduced.
Controllability properties of a class of systems modeling swimming microscopic organisms
We consider a finite-dimensional model for the motion of microscopic organisms whose propulsion exploits the action of a layer of cilia covering its surface. The model couples Newton's laws driving the organism, considered as a rigid body, with Stokes equations governing the surrounding fluid. The action of the cilia is described by a set of controlled velocity fields on the surface of the organism. The first contribution of the paper is the proof that such a system is generically controllable...
Convergence Rates of the POD–Greedy Method
Iterative approximation algorithms are successfully applied in parametric approximation tasks. In particular, reduced basis methods make use of the so-called Greedy algorithm for approximating solution sets of parametrized partial differential equations. Recently, a priori convergence rate statements for this algorithm have been given (Buffa et al. 2009, Binev et al. 2010). The goal of the current study is the extension to time-dependent problems, which are typically approximated using the POD–Greedy...
Correction to: Connecting invariant manifolds and the solution of the stability and -stability conjectures for flows.
Correction to the paper "Divergent trajectories of flows on homogeneous spaces and Diophantine approximations".
Correlation asymptotics from large deviations in dynamical systems with infinite measure
We extend a result of Doney [Probab. Theory Related Fields 107 (1997)] on renewal sequences with infinite mean to renewal sequences of operators. As a consequence, we get precise asymptotics for the transfer operator and for correlations in dynamical systems preserving an infinite measure (including intermittent maps with an arbitrarily neutral fixed point).
Corrigendum : “Almost sure rates of mixing for i.i.d. unimodal maps”
Corrigendum to the paper "Semigroup actions on tori and stationary measures on projective spaces" (Studia Math. 171 (2005), 33-66)
Countable contraction mappings in metric spaces: invariant sets and measure
We consider a complete metric space (X, d) and a countable number of contraction mappings on X, F = {F i: i ∈ ℕ}. We show the existence of a smallest invariant set (with respect to inclusion) for F. If the maps F i are of the form F i(x) = r i x + b i on X = ℝd, we prove a converse of the classic result on contraction mappings, more precisely, there exists a unique bounded invariant set if and only if r = supi r i is strictly smaller than 1. Further, if ρ = {ρ k}k∈ℕ is a probability sequence, we...