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A simple method for constructing non-liouvillian first integrals of autonomous planar systems

Axel Schulze-Halberg (2006)

Czechoslovak Mathematical Journal

We show that a transformation method relating planar first-order differential systems to second order equations is an effective tool for finding non-liouvillian first integrals. We obtain explicit first integrals for a subclass of Kukles systems, including fourth and fifth order systems, and for generalized Liénard-type systems.

Cyclic random motions in d -space with n directions

Aimé Lachal (2006)

ESAIM: Probability and Statistics

We study the probability distribution of the location of a particle performing a cyclic random motion in d . The particle can take n possible directions with different velocities and the changes of direction occur at random times. The speed-vectors as well as the support of the distribution form a polyhedron (the first one having constant sides and the other expanding with time t). The distribution of the location of the particle is made up of two components: a singular component (corresponding...

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