Bifurcation of Periodic Solutions of C5 and C6 Vector Fields in IR4 with Pure Imaginary Eigenvalues in Resonance 1:4 and 1:5
| Author | : Jaume Llibre |
| Publisher | : |
| Total Pages | : 20 |
| Release | : 2008 |
| Genre | : Averaging method (Differential equations) |
| ISBN | : |
Bifurcation Of Periodic Solutions Of C5 And C6 Vector Fields In Ir4 With Pure Imaginary Eigenvalues In Resonance 14 And 15
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Bifurcation and Symmetry
| Author | : BÖHMER |
| Publisher | : Birkhäuser |
| Total Pages | : 323 |
| Release | : 2013-03-08 |
| Genre | : Science |
| ISBN | : 3034875363 |
Symmetry is a property which occurs throughout nature and it is therefore natural that symmetry should be considered when attempting to model nature. In many cases, these models are also nonlinear and it is the study of nonlinear symmetric models that has been the basis of much recent work. Although systematic studies of nonlinear problems may be traced back at least to the pioneering contributions of Poincare, this remains an area with challenging problems for mathematicians and scientists. Phenomena whose models exhibit both symmetry and nonlinearity lead to problems which are challenging and rich in complexity, beauty and utility. In recent years, the tools provided by group theory and representation theory have proven to be highly effective in treating nonlinear problems involving symmetry. By these means, highly complex situations may be decomposed into a number of simpler ones which are already understood or are at least easier to handle. In the realm of numerical approximations, the systematic exploitation of symmetry via group repre sentation theory is even more recent. In the hope of stimulating interaction and acquaintance with results and problems in the various fields of applications, bifurcation theory and numerical analysis, we organized the conference and workshop Bifurcation and Symmetry: Cross Influences between Mathematics and Applications during June 2-7,8-14, 1991 at the Philipps University of Marburg, Germany.
Computer Algebra Methods for Equivariant Dynamical Systems
| Author | : Karin Gatermann |
| Publisher | : Springer |
| Total Pages | : 163 |
| Release | : 2007-05-06 |
| Genre | : Mathematics |
| ISBN | : 3540465197 |
This book starts with an overview of the research of Gröbner bases which have many applications in various areas of mathematics since they are a general tool for the investigation of polynomial systems. The next chapter describes algorithms in invariant theory including many examples and time tables. These techniques are applied in the chapters on symmetric bifurcation theory and equivariant dynamics. This combination of different areas of mathematics will be interesting to researchers in computational algebra and/or dynamics.
Nonlinear Oscillations and Waves in Dynamical Systems
| Author | : P.S Landa |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 550 |
| Release | : 2013-06-29 |
| Genre | : Mathematics |
| ISBN | : 9401587639 |
A rich variety of books devoted to dynamical chaos, solitons, self-organization has appeared in recent years. These problems were all considered independently of one another. Therefore many of readers of these books do not suspect that the problems discussed are divisions of a great generalizing science - the theory of oscillations and waves. This science is not some branch of physics or mechanics, it is a science in its own right. It is in some sense a meta-science. In this respect the theory of oscillations and waves is closest to mathematics. In this book we call the reader's attention to the present-day theory of non-linear oscillations and waves. Oscillatory and wave processes in the systems of diversified physical natures, both periodic and chaotic, are considered from a unified poin t of view . The relation between the theory of oscillations and waves, non-linear dynamics and synergetics is discussed. One of the purposes of this book is to convince reader of the necessity of a thorough study popular branches of of the theory of oscillat ions and waves, and to show that such science as non-linear dynamics, synergetics, soliton theory, and so on, are, in fact , constituent parts of this theory. The primary audiences for this book are researchers having to do with oscillatory and wave processes, and both students and post-graduate students interested in a deep study of the general laws and applications of the theory of oscillations and waves.
Foundations of Computational Mathematics
| Author | : Ronald A. DeVore |
| Publisher | : Cambridge University Press |
| Total Pages | : 418 |
| Release | : 2001-05-17 |
| Genre | : Mathematics |
| ISBN | : 9780521003490 |
Collection of papers by leading researchers in computational mathematics, suitable for graduate students and researchers.
New Approaches and Concepts in Turbulence
| Author | : T. Dracos |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 450 |
| Release | : 1993-09-01 |
| Genre | : Technology & Engineering |
| ISBN | : 9783764329242 |
This book contains the proceedings of a colloquium held in Monte Verità from September 9-13, 1991. Special care has been taken to devote adequate space to the scientific discussions, which claimed about half of the time available. Scientists from all over the world presented their views on the importance of kinematic properties, topology and fractal geometry, and on the dynamic behaviour of turbulent flows. They debated the importance of coherent structures and the possibility to incorporate these in the statistical theory of turbulence, as well as their significance for the reduction of the degrees of freedom and the prospective of dynamical systems and chaos approaches to the problem of turbulence. Also under discussion was the relevance of these new approaches to the study of the instability and the origin of turbulence, and the importance of numerical and physical experiments in improving the understanding of turbulence.
The Three-Body Problem and the Equations of Dynamics
| Author | : Henri Poincaré |
| Publisher | : Springer |
| Total Pages | : 265 |
| Release | : 2017-05-11 |
| Genre | : Mathematics |
| ISBN | : 3319528998 |
Here is an accurate and readable translation of a seminal article by Henri Poincaré that is a classic in the study of dynamical systems popularly called chaos theory. In an effort to understand the stability of orbits in the solar system, Poincaré applied a Hamiltonian formulation to the equations of planetary motion and studied these differential equations in the limited case of three bodies to arrive at properties of the equations’ solutions, such as orbital resonances and horseshoe orbits. Poincaré wrote for professional mathematicians and astronomers interested in celestial mechanics and differential equations. Contemporary historians of math or science and researchers in dynamical systems and planetary motion with an interest in the origin or history of their field will find his work fascinating.
Mathematics of Neural Networks
| Author | : Stephen W. Ellacott |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 438 |
| Release | : 1997-05-31 |
| Genre | : Computers |
| ISBN | : 9780792399339 |
This volume of research papers comprises the proceedings of the first International Conference on Mathematics of Neural Networks and Applications (MANNA), which was held at Lady Margaret Hall, Oxford from July 3rd to 7th, 1995 and attended by 116 people. The meeting was strongly supported and, in addition to a stimulating academic programme, it featured a delightful venue, excellent food and accommo dation, a full social programme and fine weather - all of which made for a very enjoyable week. This was the first meeting with this title and it was run under the auspices of the Universities of Huddersfield and Brighton, with sponsorship from the US Air Force (European Office of Aerospace Research and Development) and the London Math ematical Society. This enabled a very interesting and wide-ranging conference pro gramme to be offered. We sincerely thank all these organisations, USAF-EOARD, LMS, and Universities of Huddersfield and Brighton for their invaluable support. The conference organisers were John Mason (Huddersfield) and Steve Ellacott (Brighton), supported by a programme committee consisting of Nigel Allinson (UMIST), Norman Biggs (London School of Economics), Chris Bishop (Aston), David Lowe (Aston), Patrick Parks (Oxford), John Taylor (King's College, Lon don) and Kevin Warwick (Reading). The local organiser from Huddersfield was Ros Hawkins, who took responsibility for much of the administration with great efficiency and energy. The Lady Margaret Hall organisation was led by their bursar, Jeanette Griffiths, who ensured that the week was very smoothly run.
New Methods of Celestial Mechanics
| Author | : Henri Poincaré |
| Publisher | : |
| Total Pages | : 352 |
| Release | : 1967 |
| Genre | : Celestial mechanics |
| ISBN | : |
