**American Mathematical Society Translations - Series 2
Advances in the Mathematical Sciences**

2000; 196 pp; Hardcover

MSC: Primary 34; 37; Secondary 14

Print ISBN: 978-0-8218-2663-8

Product Code: TRANS2/200

Print ISBN: 978-0-8218-2663-8

Product Code: TRANS2/200

List Price: $109.00

AMS Member Price: $87.20

MAA Member Price: $98.10

**Electronic ISBN: 978-1-4704-3411-3
Product Code: TRANS2/200.E**

List Price: $109.00

AMS Member Price: $87.20

MAA Member Price: $98.10

# Methods of Qualitative Theory of Differential Equations and Related Topics

Share this page *Edited by *
*L. Lerman; G. Polotovskiĭ; L. Shilnikov*

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.

#### Readership

Graduate students, research and applied mathematicians interested in qualitative theory of differential equations; physicists.

# Table of Contents

## Methods of Qualitative Theory of Differential Equations and Related Topics

- Cover Cover11
- Frontispiece iv5
- Title page v6
- Copyright page vi7
- Contents vii8
- Evgeniya Aleksandrovna Leontovich-Andronova (1905–1996) 110
- On the abundance of traveling waves in coupled expanding circle maps 1524
- On cusp-bifurcations of periodic orbits in systems with a saddle-focus homoclinic curve 2332
- Collapse and continuity of geodesic frameworks of surface foliations 3544
- Homoclinic and heteroclinic linkages in concrete systems: Nonlocal analysis and model maps 5160
- On the mutual arrangement of a conic and a quintic in the real projective plane 6372
- The structure of the boundary curve for planar controllability domains 7382
- Orbit structure in a neighborhood of a separatrix cycle containing two saddle-foci 8796
- Example of a blue sky catastrophe 99108
- Dynamics and moduli of Ω-conjugacy of 4D-diffeomorphisms with a structurally unstable homoclinic orbit to a saddle-focus fixed point 107116
- Topological classification of amply situated attractors of 𝐴-diffeomorphisms of surfaces 135144
- A proof of Shilnikov’s theorem for 𝐶¹-smooth dynamical systems 149158
- A new simple bifurcation of a periodic orbit of “blue sky catastrophe” type 165174
- On the splitting of the complex loop of a separatrix 189198
- Back Cover Back Cover1207