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Hardcover ISBN:  9780821826638 
Product Code:  TRANS2/200 
List Price:  $175.00 
MAA Member Price:  $157.50 
AMS Member Price:  $140.00 
eBook ISBN:  9781470434113 
Product Code:  TRANS2/200.E 
List Price:  $165.00 
MAA Member Price:  $148.50 
AMS Member Price:  $132.00 
Hardcover ISBN:  9780821826638 
eBook ISBN:  9781470434113 
Product Code:  TRANS2/200.B 
List Price:  $340.00 $257.50 
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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. 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.
ReadershipGraduate students, research and applied mathematicians interested in qualitative theory of differential equations; physicists.

Table of Contents

Chapters

L. P. Shilnikov — Evgeniya Aleksandrovna LeontovichAndronova (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 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

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 saddlefoci

Nikolaĭ Gavrilov and Andrey 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

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


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

Chapters

L. P. Shilnikov — Evgeniya Aleksandrovna LeontovichAndronova (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 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

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 saddlefoci

Nikolaĭ Gavrilov and Andrey 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

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