On the genericity of chaos

Let M be a compact manifold with dimM?2. We prove that some iteration of the generic homeomorphism on M is semiconjugated to the shift map and has infinite topological entropy (Theorem 1.1).     

On existence and regularity of solutions for 2‐D micropolar fluid equations with periodic boundary conditions

In this paper, we prove the existence and uniqueness of a global solution for 2‐D micropolar fluid equation with periodic boundary conditions. Then we restrict ourselves to the autonomous case and show the existence of a global attractor. Copyright © 2006 John Wiley & Sons, Ltd.     

Chern numbers for two families of noncommutative Hopf fibrations

We consider noncommutative line bundles associated with the Hopf fibrations of SU_q(2) over all Podle? spheres and with a locally trivial Hopf fibration of S³_pq. These bundles are given as finitely generated projective modules associated via 1-dimensional representations of U(1) with Galois-type extensions encoding the principal fibrations of SU_q(2) and S³_pq. We show that the Chern numbers of these modules coincide with the winding numbers of representations defining them. To cite this article: P.M. Hajac et al., C. R. Acad. Sci. Paris, Ser. I 336 (2003).     

Global and exploding solutions in a model of self-gravitating systems

We study asymptotic properties of solutions to an extension to arbitrary dimensions of the astrophysical model proposed by Chavanis et al. to explain phenomena of gravitational collapse in clouds of self-gravitating particles. In particular, we show that in the two-dimensional case the solutions can be continued to global ones, while in three space dimensions large data of negative energy blow up in a finite time. Relations between isothermal, Streater's energy-transport and the present models are also studied.     

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Invariant measures for equicontinuous semigroups of continuous transformations of a compact Hausdorff space

Equicontinuous semigroups of transformations of a compact Hausdorff space and their sets of all invariant (Borel, regular and probabilistic) measures are studied. Conditions equivalent to the existence of at least one invariant measure are given. The (algebraic and topological) structure of the set of invariant measures is researched.     

Initiation process of L‐lactide polymerization carried out with zirconium(IV) acetylacetonate

Lactide polymerization using zirconium(IV) acetylacetonate [Zr(acac)₄] as an initiator was investigated. In the reaction between Zr(acac)₄ and the monomer molecule, lactide deprotonation and the release of acetylacetone occurred. The structures of the obtained complexes were analyzed with high‐resolution NMR spectroscopy. A computational method was used to calculate the hypothetical structures. The role of the obtained complexes in the initiation of polymerization and the reaction of chain growth was proposed. The influence of the reaction temperature on the structures of the complexes was investigated. Polylactide chain growth proceeded by an insertion‐coordination mechanism. The polymer chain grew on one ligand, which was formed in advance from a deprotonated lactide. The molecular masses of the obtained polymers were the same as the theoretical masses and were directly proportional to the reaction conversion. © 2004 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 42: 1886–1900, 2004