- 396 pages
- English
- ePUB (mobile friendly)
- Available on iOS & Android
eBook - ePub
Power Geometry in Algebraic and Differential Equations
About this book
The geometry of power exponents includes the Newton polyhedron, normal cones of its faces, power and logarithmic transformations. On the basis of the geometry universal algorithms for simplifications of systems of nonlinear equations (algebraic, ordinary differential and partial differential) were developed.The algorithms form a new calculus which allows to make local and asymptotical analysis of solutions to those systems.The efficiency of the calculus is demonstrated with regard to several complicated problems from Robotics, Celestial Mechanics, Hydrodynamics and Thermodynamics. The calculus also gives classical results obtained earlier intuitively and is an alternative to Algebraic Geometry, Differential Algebra, Lie group Analysis and Nonstandard Analysis.
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Information
Table of contents
- Cover image
- Title page
- Table of Contents
- Copyright page
- Dedication
- Preface
- Chapter 0: Introduction
- Chapter 1: The linear inequalities
- Chapter 2: Singularities of algebraic equations
- Chapter 3: Asymptotics of solutions to a system of ordinary differential equations
- Chapter 4: Hamiltonian truncations of a Hamiltonian system
- Chapter 5: Local analysis of singularities of a reversible system of ordinary differential equations
- Chapter 6: Singularities of systems of arbitrary equations
- Chapter 7: Self-similar solutions
- Chapter 8: On complexity of problems of Power Geometry
- Bibliography
- Subject index
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Yes, you can access Power Geometry in Algebraic and Differential Equations by A.D. Bruno in PDF and/or ePUB format, as well as other popular books in Mathematics & Algebraic Geometry. We have over one million books available in our catalogue for you to explore.