Poincaré-Andronov-Melnikov Analysis for Non-Smooth Systems

Michal Fečkan & Michal Pospíšil

Publisher:

Academic Press

Publication Date:

2016

Number of Pages:

244

Format:

Hardcover

Price:

199.90

ISBN:

9780128042946

Category:

Monograph

MAA Review
Table of Contents

We do not plan to review this book.

Dedication
Acknowledgment
Preface
About the Authors
An introductory example
Part I: Piecewise-smooth systems of forced ODEs
- Introduction
- Chapter I.1: Periodically forced discontinuous systems
  - I.1.1 Setting of the problem and main results
  - I.1.2 Geometric interpretation of assumed conditions
  - I.1.3 Two-position automatic pilot for ship’s controller with periodic forcing
  - I.1.4 Nonlinear planar applications
  - I.1.5 Piecewise-linear planar application
  - I.1.6 Non-smooth electronic circuits
- Chapter I.2: Bifurcation from family of periodic orbits in autonomous systems
  - I.2.1 Setting of the problem and main results
  - I.2.2 Geometric interpretation of required assumptions
  - I.2.3 On the hyperbolicity of persisting orbits
  - I.2.4 The particular case of the initial manifold
  - I.2.5 3-dimensional piecewise-linear application
  - I.2.6 Coupled Van der Pol and harmonic oscillators at 1-1 resonance
- Chapter I.3: Bifurcation from single periodic orbit in autonomous systems
  - I.3.1 Setting of the problem and main results
  - I.3.2 The special case for linear switching manifold
  - I.3.3 Planar application
  - I.3.4 Formulae for the second derivatives
- Chapter I.4: Sliding solution of periodically perturbed systems
  - I.4.1 Setting of the problem and main results
  - I.4.2 Piecewise-linear application
- Chapter I.5: Weakly coupled oscillators
  - I.5.1 Setting of the problem
  - I.5.2 Bifurcations from single periodic solutions
  - I.5.3 Bifurcations from families of periodics
  - I.5.4 Examples
- Reference
Part II: Forced hybrid systems
- Introduction
- Chapter II.1: Periodically forced impact systems
  - II.1.1 Setting of the problem and main results
- Chapter II.2: Bifurcation from family of periodic orbits in forced billiards
  - II.2.1 Setting of the problem and main results
  - II.2.2 Application to a billiard in a circle
- Reference
Part III: Continuous approximations of non-smooth systems
- Introduction
- Chapter III.1: Transversal periodic orbits
  - III.1.1 Setting of the problem and main result
  - III.1.2 Approximating bifurcation functions
  - III.1.3 Examples
- Chapter III.2: Sliding periodic orbits
  - III.2.1 Setting of the problem
  - III.2.2 Planar illustrative examples
  - III.2.3 Higher dimensional systems
  - III.2.4 Examples
- Chapter III.3: Impact periodic orbits
  - III.3.1 Setting of the problem
  - III.3.2 Bifurcation equation
  - III.3.3 Bifurcation from a single periodic solution
  - III.3.4 Poincaré-Andronov-Melnikov function and adjoint system
  - III.3.5 Bifurcation from a manifold of periodic solutions
- Chapter III.4: Approximation and dynamics
  - III.4.1 Asymptotic properties under approximation
  - III.4.2 Application to pendulum with dry friction
- Reference
Appendix A
- A.1 Nonlinear functional analysis
- A.2 Multivalued mappings
- A.3 Singularly perturbed ODEs
- A.4 Note on Lyapunov theorem for Hill’s equation
Bibliography
Index