Planar Dynamical Systems :
Liu, Yirong,
Planar Dynamical Systems : Selected Classical Problems / Yirong Liu, Jibin Li, Wentao Huang. - Berlin ; Boston : De Gruyter, [2014] ©2014 - 1 online resource (389 p.)
Frontmatter -- Preface -- Contents -- Chapter 1. Basic Concept and Linearized Problem of Systems -- Chapter 2. Focal Values, Saddle Values and Singular Point Values -- Chapter 3. Multiple Hopf Bifurcations -- Chapter 4. Isochronous Center In Complex Domain -- Chapter 5. Theory of Center-Focus and Bifurcation of Limit Cycles at Infinity of a Class of Systems -- Chapter 6. Theory of Center-Focus and Bifurcations of Limit Cycles for a Class of Multiple Singular Points -- Chapter 7 On Quasi Analytic Systems -- Chapter 8. Local and Non-Local Bifurcations of Perturbed Zq-Equivariant Hamiltonian Vector Fields -- Chapter 9. Center-Focus Problem and Bifurcations of Limit Cycles for a Z2-Equivariant Cubic System -- Chapter 10. Center-Focus Problem and Bifurcations of Limit Cycles for Three-Multiple Nilpotent Singular Points -- Bibliography -- Index
Open Access https://purl.org/coar/access_right/c_abf2
In 2008, November 23-28, the workshop of "Classical Problems on Planar Polynomial Vector Fields " was held in the Banff International Research Station, Canada. Called "classical problems", it was concerned with the following: (1) Problems on integrability of planar polynomial vector fields. (2) The problem of the center stated by Poincaré for real polynomial differential systems, which asks us to recognize when a planar vector field defined by polynomials of degree at most n possesses a singularity which is a center. (3) Global geometry of specific classes of planar polynomial vector fields. (4) Hilbert's 16th problem. These problems had been posed more than 110 years ago. Therefore, they are called "classical problems" in the studies of the theory of dynamical systems. The qualitative theory and stability theory of differential equations, created by Poincaré and Lyapunov at the end of the 19th century, had major developments as two branches of the theory of dynamical systems during the 20th century. As a part of the basic theory of nonlinear science, it is one of the very active areas in the new millennium. This book presents in an elementary way the recent significant developments in the qualitative theory of planar dynamical systems. The subjects are covered as follows: the studies of center and isochronous center problems, multiple Hopf bifurcations and local and global bifurcations of the equivariant planar vector fields which concern with Hilbert's 16th problem. The book is intended for graduate students, post-doctors and researchers in dynamical systems. For all engineers who are interested in the theory of dynamical systems, it is also a reasonable reference. It requires a minimum background of a one-year course on nonlinear differential equations.
Mode of access: Internet via World Wide Web.
This eBook is made available Open Access under a CC BY-NC-ND 4.0 license:
In English.
9783110298369
10.1515/9783110298369 doi
Differential equations.
Dynamics.
Center and isochronous center.
Dynamical Systems.
Hilbert's 16th problem.
Limit cycle.
Multiple Hopf and global bifurcations.
Planar Dynamical Systems.
Planar dynamical system.
center problems.
multiple Hopf bifurcations.
MATHEMATICS / Applied.
QA845 / .L58 2014eb
510
Planar Dynamical Systems : Selected Classical Problems / Yirong Liu, Jibin Li, Wentao Huang. - Berlin ; Boston : De Gruyter, [2014] ©2014 - 1 online resource (389 p.)
Frontmatter -- Preface -- Contents -- Chapter 1. Basic Concept and Linearized Problem of Systems -- Chapter 2. Focal Values, Saddle Values and Singular Point Values -- Chapter 3. Multiple Hopf Bifurcations -- Chapter 4. Isochronous Center In Complex Domain -- Chapter 5. Theory of Center-Focus and Bifurcation of Limit Cycles at Infinity of a Class of Systems -- Chapter 6. Theory of Center-Focus and Bifurcations of Limit Cycles for a Class of Multiple Singular Points -- Chapter 7 On Quasi Analytic Systems -- Chapter 8. Local and Non-Local Bifurcations of Perturbed Zq-Equivariant Hamiltonian Vector Fields -- Chapter 9. Center-Focus Problem and Bifurcations of Limit Cycles for a Z2-Equivariant Cubic System -- Chapter 10. Center-Focus Problem and Bifurcations of Limit Cycles for Three-Multiple Nilpotent Singular Points -- Bibliography -- Index
Open Access https://purl.org/coar/access_right/c_abf2
In 2008, November 23-28, the workshop of "Classical Problems on Planar Polynomial Vector Fields " was held in the Banff International Research Station, Canada. Called "classical problems", it was concerned with the following: (1) Problems on integrability of planar polynomial vector fields. (2) The problem of the center stated by Poincaré for real polynomial differential systems, which asks us to recognize when a planar vector field defined by polynomials of degree at most n possesses a singularity which is a center. (3) Global geometry of specific classes of planar polynomial vector fields. (4) Hilbert's 16th problem. These problems had been posed more than 110 years ago. Therefore, they are called "classical problems" in the studies of the theory of dynamical systems. The qualitative theory and stability theory of differential equations, created by Poincaré and Lyapunov at the end of the 19th century, had major developments as two branches of the theory of dynamical systems during the 20th century. As a part of the basic theory of nonlinear science, it is one of the very active areas in the new millennium. This book presents in an elementary way the recent significant developments in the qualitative theory of planar dynamical systems. The subjects are covered as follows: the studies of center and isochronous center problems, multiple Hopf bifurcations and local and global bifurcations of the equivariant planar vector fields which concern with Hilbert's 16th problem. The book is intended for graduate students, post-doctors and researchers in dynamical systems. For all engineers who are interested in the theory of dynamical systems, it is also a reasonable reference. It requires a minimum background of a one-year course on nonlinear differential equations.
Mode of access: Internet via World Wide Web.
This eBook is made available Open Access under a CC BY-NC-ND 4.0 license:
In English.
9783110298369
10.1515/9783110298369 doi
Differential equations.
Dynamics.
Center and isochronous center.
Dynamical Systems.
Hilbert's 16th problem.
Limit cycle.
Multiple Hopf and global bifurcations.
Planar Dynamical Systems.
Planar dynamical system.
center problems.
multiple Hopf bifurcations.
MATHEMATICS / Applied.
QA845 / .L58 2014eb
510