Geodesic flows are of considerable current interest since they are,
perhaps, the most remarkable class of conservative dynamical systems.
They provide a unified arena in which one can explore numerous interplays among several fields,
including smooth ergodic theory, symplectic and Riemannian geometry, and algebraic topology.
The book will be interest to graduate students and researchers of dynamical systems
and differential geometry and can be used as a text for a one-semester Course or Seminar.
Sep. 1999 168 pp.
3-7643-4144-0 10,290.
Differential Galois Theory and
Non-integrability of Hamiltonian Systems
Ferran Sunyer i Balaguer Prize 1998!
This award-winning monograph is devoted to the relation between
two different concepts of integrability leading to algebraic non-integrability criteria for Hamiltonian systems.
These criteria can be considered generalizations of classical non-integrability results by
Poincare and Liapunov, as well as more recent results by Ziglin and Yoshida.
Several non-mathematical applications are given:
homogeneous potentials, Bianchi lX cosmological model, three-body problem,
Henon-Heiles system, etc.
The necessary background on differential Galois theory and
Hamiltonian systems is included, and several new problems and
conjectures which open new lines of research are proposed.
Aug. 1999 180 pp.
3-7643-6078-X 10,290
Metric Structures for Riemannian and Non-Riemannian Spaces
The boundary of metric theory, which covers a domain between
the fields of topology and global Riemannian geometry, has dramaticatly exploded in the last 20 years,
in part due to the im-portant research of one of the vvorldi leading geometers, M. Gromov.
"Metric Structures for Riemannian and Non-Riemannian Spaces"
is based on an earlier French work (1979) which has been substantially revised and expanded.
Exciting new connections between geometry
and probability theoTy are made and links to analysis are developed.
Key ideas of real analysis are presented in an accessible way to geometers.
This self-contained monograph may be used in seminars and topics courses.
Numerous illustrations and examples, bibliography and index,
accompany a well-written text, which is an
excellent self-study resource for geometers, analysts, and probabilists.
July 1999 599 pp.
3-7643-3898-9 21,180.