16,346 research outputs found
Invariant Regions and Global Asymptotic Stability in an Isothermal Catalyst
A well-known model for the evolution of the (space-dependent) concentration and (lumped) temperature in a porous catalyst is considered. A sequence of invariant regions of the phase space is given, which converges to a globally asymptotically stable region . Quantitative sufficient conditions are obtained for (the region to consist of only one point and) the problem to have a (unique) globally asymptotically stable steady state
On ergodic operator means in Banach spaces
We consider a large class of operator means and prove that a number of
ergodic theorems, as well as growth estimates known for particular cases,
continue to hold in the general context under fairly mild regularity
conditions. The methods developed in the paper not only yield a new approach
based on a general point of view, but also lead to results that are new, even
in the context of the classical Cesaro means
Finsler bordifications of symmetric and certain locally symmetric spaces
We give a geometric interpretation of the maximal Satake compactification of
symmetric spaces of noncompact type, showing that it arises by
attaching the horofunction boundary for a suitable -invariant Finsler metric
on . As an application, we establish the existence of natural
bordifications, as orbifolds-with-corners, of locally symmetric spaces
for arbitrary discrete subgroups . These bordifications
result from attaching -quotients of suitable domains of proper
discontinuity at infinity. We further prove that such bordifications are
compactifications in the case of Anosov subgroups. We show, conversely, that
Anosov subgroups are characterized by the existence of such compactifications
among uniformly regular subgroups. Along the way, we give a positive answer, in
the torsion free case, to a question of Ha\"issinsky and Tukia on convergence
groups regarding the cocompactness of their actions on the domains of
discontinuity.Comment: 88 page
Exponential inequalities and functional estimations for weak dependent datas ; applications to dynamical systems
We estimate density and regression functions for weak dependant datas. Using
an exponential inequality obtained by Dedecker and Prieur and in a previous
article of the author, we control the deviation between the estimator and the
function itself. These results are applied to a large class of dynamical
systems and lead to estimations of invariant densities and on the mapping
itself
Minimality properties of set-valued processes and their pullback attractors
We discuss the existence of pullback attractors for multivalued dynamical
systems on metric spaces. Such attractors are shown to exist without any
assumptions in terms of continuity of the solution maps, based only on
minimality properties with respect to the notion of pullback attraction. When
invariance is required, a very weak closed graph condition on the solving
operators is assumed. The presentation is complemented with examples and
counterexamples to test the sharpness of the hypotheses involved, including a
reaction-diffusion equation, a discontinuous ordinary differential equation and
an irregular form of the heat equation.Comment: 33 pages. A few typos correcte
Existence of critical subsolutions in discrete weak KAM theory
In this article, following a first work of the author, we study critical
subsolutions in discrete weak KAM theory. In particular, we establish that if
the cost function defined on a smooth connected manifold
is locally semi-concave and verifies twist conditions, then there exists a
critical subsolution strict on a maximal set (namely, outside of the
Aubry set). We also explain how this applies to costs coming from Tonelli
Lagrangians. Finally, following ideas introduced in the work of Fathi-Maderna
and Mather, we study invariant cost functions and apply this study to certain
covering spaces, introducing a discrete analogue of Mather's function
on the cohomology.Comment: 28 page
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