American Mathematical Society TranslationsSeries 2 Advances in the Mathematical Sciences 2000; 196 pp; hardcover Volume: 200 ISBN10: 0821826638 ISBN13: 9780821826638 List Price: US$109 Member Price: US$87.20 Order Code: TRANS2/200
 Dedicated to the memory of Professor E. A. LeontovichAndronova, this book was composed by former students and colleagues who wished to mark her contributions to the theory of dynamical systems. A detailed introduction by LeontovichAndronova's close colleague, L. Shilnikov, presents biographical data and describes her main contribution to the theory of bifurcations and dynamical systems. The main part of the volume is composed of research papers presenting the interests of LeontovichAndronova, her students and her colleagues. Included are articles on traveling waves in coupled circle maps, bifurcations near a homoclinic orbit, polynomial quadratic systems on the plane, foliations on surfaces, homoclinic bifurcations in concrete systems, topology of plane controllability regions, separatrix cycle with two saddlefoci, dynamics of 4dimensional symplectic maps, torus maps from strong resonances, structure of 3 degreeoffreedom integrable Hamiltonian systems, splitting separatrices in complex differential equations, Shilnikov's bifurcation for \(C^1\)smooth systems and "blue sky catastrophe" for periodic orbits. Readership Graduate students, research and applied mathematicians interested in qualitative theory of differential equations; physicists. Table of Contents  L. P. Shilnikov  Evgeniya Aleksandrovna LeontovichAndronova (19051996)
 V. Afraimovich and M. Courbage  On the abundance of traveling waves in coupled expanding circle maps
 S. A. Alekseeva and L. P. Shilnikov  On cuspbifurcations of periodic orbits in systems with a saddlefocus homoclinic curve
 S. Aranson, V. Medvedev, and E. Zhuzhoma  Collapse and continuity of geodesic frameworks of surface foliations
 V. N. Belykh  Homoclinic and heteroclinic linkages in concrete systems: Nonlocal analysis and model maps
 A. A. Binstein and G. M. Polotovskiĭ  On the mutual arrangement of a conic and a quintic in the real projective plane
 N. N. Butenina  The structure of the boundary curve for planar controllability domains
 V. V. Bykov  Orbit structure in a neighborhood of a separatrix cycle containing two saddlefoci
 N. Gavrilov and A. Shilnikov  Example of a blue sky catastrophe
 S. V. Gonchenko  Dynamics and moduli of \(\Omega\)conjugacy of 4Ddiffeomorphisms with a structurally unstable homoclinic orbit to a saddlefocus fixed point
 V. Z. Grines and R. V. Plykin  Topological classification of amply situated attractors of \(A\)diffeomorphisms of surfaces
 M. V. Shashkov and D. V. Turaev  A proof of Shilnikov's theorem for \(C^1\)smooth dynamical systems
 L. P. Shilnikov and D. V. Turaev  A new simple bifurcation of a periodic orbit of "blue sky catastrophe" type
 V. P. Tareev  On the splitting of the complex loop of a separatrix
 A. A. E.  Some topological structures of quadratic systems with at least four limit cycles
 J. Guckenheimer and I. Khibnik  Torus maps from weak coupling of strong resonances
 L. M. Lerman  Isoenergetical structure of integrable Hamiltonian systems in an extended neighborhood of a simple singular point: Three degrees of freedom
