Dedicated to the memory of Professor E. A. Leontovich-Andronova, 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 Leontovich-Andronova'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 Leontovich-Andronova, 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 saddle-foci, dynamics of 4-dimensional symplectic maps, torus maps from strong resonances, structure of 3 degree-of-freedom integrable Hamiltonian systems, splitting separatrices in complex differential equations, Shilnikov's bifurcation for $C^1$-smooth systems and 'blue sky catastrophe' for periodic orbits.

Table of Contents:
Evgeniya Aleksandrovna Leontovich-Andronova (1905-1996) by L. P. Shilnikov On the abundance of traveling waves in coupled expanding circle maps by V. Afraimovich and M. Courbage On cusp-bifurcations of periodic orbits in systems with a saddle-focus homoclinic curve by S. A. Alekseeva and L. P. Shilnikov Collapse and continuity of geodesic frameworks of surface foliations by S. Aranson, V. Medvedev, and E. Zhuzhoma Homoclinic and heteroclinic linkages in concrete systems: Nonlocal analysis and model maps by V. N. Belykh On the mutual arrangement of a conic and a quintic in the real projective plane by A. A. Binstein and G. M. Polotovskii The structure of the boundary curve for planar controllability domains by N. N. Butenina Orbit structure in a neighborhood of a separatrix cycle containing two saddle-foci by V. V. Bykov Example of a blue sky catastrophe by N. Gavrilov and A. Shilnikov Dynamics and moduli of $\Omega$-conjugacy of 4D-diffeomorphisms with a structurally unstable homoclinic orbit to a saddle-focus fixed point by S. V. Gonchenko Topological classification of amply situated attractors of $A$-diffeomorphisms of surfaces by V. Z. Grines and R. V. Plykin A proof of Shilnikov's theorem for $C^1$-smooth dynamical systems by M. V. Shashkov and D. V. Turaev A new simple bifurcation of a periodic orbit of "blue sky catastrophe" type by L. P. Shilnikov and D. V. Turaev On the splitting of the complex loop of a separatrix by V. P. Tareev Some topological structures of quadratic systems with at least four limit cycles by A. A. E. Torus maps from weak coupling of strong resonances by J. Guckenheimer and I. Khibnik Isoenergetical structure of integrable Hamiltonian systems in an extended neighborhood of a simple singular point: Three degrees of freedom by L. M. Lerman.