Methods of Qualitative Theory of Differential Equations and Related Topics ( American Mathematical Society Translations - Series 2 )

Publication series ：American Mathematical Society Translations - Series 2

Author： L. Lerman;G. Polotovskiĭ;L. Shilnikov

Publisher： American Mathematical Society‎

Publication year： 2000

E-ISBN: 9781470434113

P-ISBN(Hardback): 9780821826638

Subject： O175 differential equations, integral equations

Keyword：暂无分类

Language： ENG

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Methods of Qualitative Theory of Differential Equations and Related Topics

Description

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.

Chapter

Cover

Frontispiece

Title page

Contents

Evgeniya Aleksandrovna Leontovich-Andronova (1905–1996)

On the abundance of traveling waves in coupled expanding circle maps

On cusp-bifurcations of periodic orbits in systems with a saddle-focus homoclinic curve

Collapse and continuity of geodesic frameworks of surface foliations

Homoclinic and heteroclinic linkages in concrete systems: Nonlocal analysis and model maps

On the mutual arrangement of a conic and a quintic in the real projective plane

The structure of the boundary curve for planar controllability domains

Orbit structure in a neighborhood of a separatrix cycle containing two saddle-foci

Example of a blue sky catastrophe

Dynamics and moduli of Ω-conjugacy of 4D-diffeomorphisms with a structurally unstable homoclinic orbit to a saddle-focus fixed point

Topological classification of amply situated attractors of 𝐴-diffeomorphisms of surfaces

A proof of Shilnikov’s theorem for 𝐶¹-smooth dynamical systems

A new simple bifurcation of a periodic orbit of “blue sky catastrophe” type

On the splitting of the complex loop of a separatrix

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