On the regularity of the composition of

diffeomorphisms.

This interpretation restricts allowable

diffeomorphisms to only those preserving the four volume, but to date this has been treated as but a curious equivalent to General Relativity.

The topics are local holomorphic dynamics of

diffeomorphisms in dimension one, non-positive curvature and complex analysis, Virasoro algebra and dynamics in the space of univalent functions, composition operators love Toeplitz operators, and two applications of the Bergman spaces techniques.

The interesting, but restrictive, algebraic structure of the model, containing a 3-algebra with antisymmetric structure constants, turned out to have only one finite-dimensional realization [24,25], possible to interpret in terms of two M2-branes [26,27] (see, however, [28-30] dealing with the infinite-dimensional solution related to volume-preserving

diffeomorphisms in three dimensions).

Deterministic viscous hydrodynamics via stochastic processes on groups of

diffeomorphisms, Probabilistic Metohds in Fluids (I.

To show that the same results take place for

diffeomorphisms also, let us consider the following maps of [R.

BOWEN, Equilibrium States and the Ergodic Theory of Anosov

Diffeomorphisms, Lecture Notes in Mathematics, 470, Springer-Verlag, Berlinr, 1975.

The 19 papers based on lectures given at the July 2012 conference share new developments in p-adicq-distributions, partial fractional differentiability, generalized Keller spaces over valued fields, branched values for p-adicmeromorphic functions, and Grobman-Hartman theorems for

diffeomorphisms of Banach spaces over valued fields.

m] and M f be the category of m-dimensional manifolds endowed with local

diffeomorphisms and the category of all manifolds and all smooth mappings, respectively.

Six papers cover a Hofer-like metric on the group of symplectic

diffeomorphisms; the C0-rigidity of Poisson brackets; six questions, a proposition, and two pictures on Hofer distance for Hamiltonian

diffeomorphisms on surfaces; order structure on action-minimizing orbits; a survey of loops in the Hamiltonian group; and the group of Hamiltonian homeomorphisms and continuous Hamiltonian flows.

The topics include topologies on spaces of dynamical systems, the hyperbolic fixed point, transversality, Anosov

diffeomorphisms, and the shadowing of pseudo-trajectories in dynamical systems.

Groups of

diffeomorphisms in honor of Shigeyuki Morita on the occasion of his 60th birthday; proceedings.