Regularity of the solutions of second order evolution equations and their attractors
Regularity of topological and metric entropy of hyperbolic flows.
Regularity of weak KAM solutions and Mañé’s Conjecture
We provide a crash course in weak KAM theory and review recent results concerning the existence and uniqueness of weak KAM solutions and their link with the so-called Mañé conjecture.
Regularization of currents and entropy
Reidemeister torsion and integrable Hamiltonian systems.
Relación entre las pseudo-métricas quasi-kaehlerianas y las semi-foliadas.
Relating Hausdorff measures and harmonic measures on parabolic Jordan curves.
Relationship between different types of stability for linear almost periodic systems in Banach spaces.
Relative generic singularities of the exponential map
Relative property (T) and linear groups
Relative property (T) has recently been used to show the existence of a variety of new rigidity phenomena, for example in von Neumann algebras and the study of orbit-equivalence relations. However, until recently there were few examples of group pairs with relative property (T) available through the literature. This motivated the following result: A finitely generated group admits a special linear representation with non-amenable -Zariski closure if and only if it acts on an Abelian group (of...
Relative spectral theory and measure-theoretic entropy of gaussian extensions
We describe the natural framework in which the relative spectral theory is developed. We give some results and indicate how they relate to two open problems in ergodic theory. We also compute the relative entropy of gaussian extensions of ergodic transformations.
Relativistic stability of matter (I).
In this article, we study the quantum mechanics of N electrons and M nuclei interacting by Coulomb forces. Motivated by an important idea of Chandrasekhar and following Herbst [H], we modify the usual kinetic energy -∆ to take into account an effect from special relativity. As a result, the system can implode for unfavorable values of the nuclear charge Z and the fine structure constant α. This is analogous to the gravitational collapse of a heavy star. Our goal here is to find those values of α...
Relativity and irreversibility.
Remarks on dynamical systems with weak forces.
Remarks on iterated cubic maps.
Remarks on some monotonicity conditions for the period function
We are interested in the optimality of monotonicity criteria for the period function of some planar Hamiltonian systems. This study is illustrated by examples.
Remarks on the Darboux transform of isothermic surfaces.
Remarks on the Lichnerowicz-Poisson cohomology
The paper begins with some general remarks which include the Mayer-Vietoris exact sequence, a covariant version of the Lichnerowicz-Poisson cohomology, and the definition of an associated Serre-Hochshild spectral sequence. Then we consider the regular case, and we discuss the Poisson cohomology by using a natural bigrading of the Lichnerowicz cochain complex. Furthermore, if the symplectic foliation of the Poisson manifold is either transversally Riemannian or transversally symplectic, the spectral...
Remarks on the region of attraction of an isolated invariant set
We study the complexity of the flow in the region of attraction of an isolated invariant set. More precisely, we define the instablity depth, which is an ordinal and measures how far an isolated invariant set is from being asymptotically stable within its region of attraction. We provide upper and lower bounds of the instability depth in certain cases.
Remarks on the simple connectedness of basins of sinks for iterations of rational maps