| Hardcover ISBN: | 978-0-8218-2663-8 |
| Product Code: | TRANS2/200 |
| List Price: | $175.00 |
| MAA Member Price: | $157.50 |
| AMS Member Price: | $140.00 |
| eBook ISBN: | 978-1-4704-3411-3 |
| Product Code: | TRANS2/200.E |
| List Price: | $165.00 |
| MAA Member Price: | $148.50 |
| AMS Member Price: | $132.00 |
| Hardcover ISBN: | 978-0-8218-2663-8 |
| eBook: ISBN: | 978-1-4704-3411-3 |
| Product Code: | TRANS2/200.B |
| List Price: | $340.00 $257.50 |
| MAA Member Price: | $306.00 $231.75 |
| AMS Member Price: | $272.00 $206.00 |
| Hardcover ISBN: | 978-0-8218-2663-8 |
| Product Code: | TRANS2/200 |
| List Price: | $175.00 |
| MAA Member Price: | $157.50 |
| AMS Member Price: | $140.00 |
| eBook ISBN: | 978-1-4704-3411-3 |
| Product Code: | TRANS2/200.E |
| List Price: | $165.00 |
| MAA Member Price: | $148.50 |
| AMS Member Price: | $132.00 |
| Hardcover ISBN: | 978-0-8218-2663-8 |
| eBook ISBN: | 978-1-4704-3411-3 |
| Product Code: | TRANS2/200.B |
| List Price: | $340.00 $257.50 |
| MAA Member Price: | $306.00 $231.75 |
| AMS Member Price: | $272.00 $206.00 |
-
Book DetailsAmerican Mathematical Society Translations - Series 2Advances in the Mathematical SciencesVolume: 200; 2000; 196 ppMSC: Primary 34; 37; Secondary 14
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.
ReadershipGraduate students, research and applied mathematicians interested in qualitative theory of differential equations; physicists.
-
Table of Contents
-
Chapters
-
L. P. Shilnikov — Evgeniya Aleksandrovna Leontovich-Andronova (1905–1996)
-
V. Afraimovich and M. Courbage — On the abundance of traveling waves in coupled expanding circle maps
-
S. A. Alekseeva and L. P. Shilnikov — On cusp-bifurcations of periodic orbits in systems with a saddle-focus homoclinic curve
-
S. Aranson, V. Medvedev and E. Zhuzhoma — Collapse and continuity of geodesic frameworks of surface foliations
-
Vladimir N. Belykh — Homoclinic and heteroclinic linkages in concrete systems: Nonlocal analysis and model maps
-
Anna A. Binstein and Grigoriĭ 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 saddle-foci
-
Nikolaĭ Gavrilov and Andrey Shilnikov — Example of a blue sky catastrophe
-
S. V. Gonchenko — Dynamics and moduli of $\Omega $-conjugacy of 4D-diffeomorphisms with a structurally unstable homoclinic orbit to a saddle-focus fixed point
-
V. Z. Grines and R. V. Plykin — Topological classification of amply situated attractors of $A$-diffeomorphisms of surfaces
-
Mikhail V. Shashkov and Dmitry V. Turaev — A proof of Shilnikov’s theorem for $C^1$-smooth dynamical systems
-
Leonid P. Shilnikov and Dmitry 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
-
-
RequestsReview Copy – for publishers of book reviewsPermission – for use of book, eBook, or Journal contentAccessibility – to request an alternate format of an AMS title
- Book Details
- Table of Contents
- Requests
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.
Graduate students, research and applied mathematicians interested in qualitative theory of differential equations; physicists.
-
Chapters
-
L. P. Shilnikov — Evgeniya Aleksandrovna Leontovich-Andronova (1905–1996)
-
V. Afraimovich and M. Courbage — On the abundance of traveling waves in coupled expanding circle maps
-
S. A. Alekseeva and L. P. Shilnikov — On cusp-bifurcations of periodic orbits in systems with a saddle-focus homoclinic curve
-
S. Aranson, V. Medvedev and E. Zhuzhoma — Collapse and continuity of geodesic frameworks of surface foliations
-
Vladimir N. Belykh — Homoclinic and heteroclinic linkages in concrete systems: Nonlocal analysis and model maps
-
Anna A. Binstein and Grigoriĭ 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 saddle-foci
-
Nikolaĭ Gavrilov and Andrey Shilnikov — Example of a blue sky catastrophe
-
S. V. Gonchenko — Dynamics and moduli of $\Omega $-conjugacy of 4D-diffeomorphisms with a structurally unstable homoclinic orbit to a saddle-focus fixed point
-
V. Z. Grines and R. V. Plykin — Topological classification of amply situated attractors of $A$-diffeomorphisms of surfaces
-
Mikhail V. Shashkov and Dmitry V. Turaev — A proof of Shilnikov’s theorem for $C^1$-smooth dynamical systems
-
Leonid P. Shilnikov and Dmitry 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
