Author: H.-O. Peitgen
Publisher: Springer Science & Business Media
ISBN: 9400922817
Category : Science
Languages : en
Pages : 227
Book Description
Newton’s Method and Dynamical Systems
Author: H.-O. Peitgen
Publisher: Springer Science & Business Media
ISBN: 9400922817
Category : Science
Languages : en
Pages : 227
Book Description
Publisher: Springer Science & Business Media
ISBN: 9400922817
Category : Science
Languages : en
Pages : 227
Book Description
Newton's Method and Dynamical Systems
Author: Jianping Yang
Publisher:
ISBN:
Category : Differentiable dynamical systems
Languages : en
Pages : 186
Book Description
Publisher:
ISBN:
Category : Differentiable dynamical systems
Languages : en
Pages : 186
Book Description
Special Issue on Newton's Method and Dynamical Systems
Author: Heinz-Otto Peitgen
Publisher:
ISBN:
Category :
Languages : en
Pages : 226
Book Description
Publisher:
ISBN:
Category :
Languages : en
Pages : 226
Book Description
Dynamical Systems and Fractals
Author: Karl-Heinz Becker
Publisher: Cambridge University Press
ISBN: 9780521369107
Category : Computers
Languages : en
Pages : 420
Book Description
This 1989 book is about chaos, fractals and complex dynamics.
Publisher: Cambridge University Press
ISBN: 9780521369107
Category : Computers
Languages : en
Pages : 420
Book Description
This 1989 book is about chaos, fractals and complex dynamics.
Newton's Method as a Dynamical System
Author: Johannes Rückert
Publisher:
ISBN:
Category :
Languages : en
Pages :
Book Description
Publisher:
ISBN:
Category :
Languages : en
Pages :
Book Description
A First Course In Chaotic Dynamical Systems
Author: Robert L. Devaney
Publisher: CRC Press
ISBN: 0429983115
Category : Mathematics
Languages : en
Pages : 386
Book Description
A First Course in Chaotic Dynamical Systems: Theory and Experiment is the first book to introduce modern topics in dynamical systems at the undergraduate level. Accessible to readers with only a background in calculus, the book integrates both theory and computer experiments into its coverage of contemporary ideas in dynamics. It is designed as a gradual introduction to the basic mathematical ideas behind such topics as chaos, fractals, Newton's method, symbolic dynamics, the Julia set, and the Mandelbrot set, and includes biographies of some of the leading researchers in the field of dynamical systems. Mathematical and computer experiments are integrated throughout the text to help illustrate the meaning of the theorems presented. Chaotic Dynamical Systems Software, Labs 1-6 is a supplementary labouratory software package, available separately, that allows a more intuitive understanding of the mathematics behind dynamical systems theory. Combined with A First Course in Chaotic Dynamical Systems , it leads to a rich understanding of this emerging field.
Publisher: CRC Press
ISBN: 0429983115
Category : Mathematics
Languages : en
Pages : 386
Book Description
A First Course in Chaotic Dynamical Systems: Theory and Experiment is the first book to introduce modern topics in dynamical systems at the undergraduate level. Accessible to readers with only a background in calculus, the book integrates both theory and computer experiments into its coverage of contemporary ideas in dynamics. It is designed as a gradual introduction to the basic mathematical ideas behind such topics as chaos, fractals, Newton's method, symbolic dynamics, the Julia set, and the Mandelbrot set, and includes biographies of some of the leading researchers in the field of dynamical systems. Mathematical and computer experiments are integrated throughout the text to help illustrate the meaning of the theorems presented. Chaotic Dynamical Systems Software, Labs 1-6 is a supplementary labouratory software package, available separately, that allows a more intuitive understanding of the mathematics behind dynamical systems theory. Combined with A First Course in Chaotic Dynamical Systems , it leads to a rich understanding of this emerging field.
Newton's Method Applied to Two Quadratic Equations in $\mathbb {C}^2$ Viewed as a Global Dynamical System
Author: John H. Hubbard
Publisher: American Mathematical Soc.
ISBN: 0821840568
Category : Mathematics
Languages : en
Pages : 160
Book Description
The authors study the Newton map $N:\mathbb{C}^2\rightarrow\mathbb{C}^2$ associated to two equations in two unknowns, as a dynamical system. They focus on the first non-trivial case: two simultaneous quadratics, to intersect two conics. In the first two chapters, the authors prove among other things: The Russakovksi-Shiffman measure does not change the points of indeterminancy. The lines joining pairs of roots are invariant, and the Julia set of the restriction of $N$ to such a line has under appropriate circumstances an invariant manifold, which shares features of a stable manifold and a center manifold. The main part of the article concerns the behavior of $N$ at infinity. To compactify $\mathbb{C}^2$ in such a way that $N$ extends to the compactification, the authors must take the projective limit of an infinite sequence of blow-ups. The simultaneous presence of points of indeterminancy and of critical curves forces the authors to define a new kind of blow-up: the Farey blow-up. This construction is studied in its own right in chapter 4, where they show among others that the real oriented blow-up of the Farey blow-up has a topological structure reminiscent of the invariant tori of the KAM theorem. They also show that the cohomology, completed under the intersection inner product, is naturally isomorphic to the classical Sobolev space of functions with square-integrable derivatives. In chapter 5 the authors apply these results to the mapping $N$ in a particular case, which they generalize in chapter 6 to the intersection of any two conics.
Publisher: American Mathematical Soc.
ISBN: 0821840568
Category : Mathematics
Languages : en
Pages : 160
Book Description
The authors study the Newton map $N:\mathbb{C}^2\rightarrow\mathbb{C}^2$ associated to two equations in two unknowns, as a dynamical system. They focus on the first non-trivial case: two simultaneous quadratics, to intersect two conics. In the first two chapters, the authors prove among other things: The Russakovksi-Shiffman measure does not change the points of indeterminancy. The lines joining pairs of roots are invariant, and the Julia set of the restriction of $N$ to such a line has under appropriate circumstances an invariant manifold, which shares features of a stable manifold and a center manifold. The main part of the article concerns the behavior of $N$ at infinity. To compactify $\mathbb{C}^2$ in such a way that $N$ extends to the compactification, the authors must take the projective limit of an infinite sequence of blow-ups. The simultaneous presence of points of indeterminancy and of critical curves forces the authors to define a new kind of blow-up: the Farey blow-up. This construction is studied in its own right in chapter 4, where they show among others that the real oriented blow-up of the Farey blow-up has a topological structure reminiscent of the invariant tori of the KAM theorem. They also show that the cohomology, completed under the intersection inner product, is naturally isomorphic to the classical Sobolev space of functions with square-integrable derivatives. In chapter 5 the authors apply these results to the mapping $N$ in a particular case, which they generalize in chapter 6 to the intersection of any two conics.
Solving Nonlinear Equations with Newton's Method
Author: C. T. Kelley
Publisher: SIAM
ISBN: 9780898718898
Category : Mathematics
Languages : en
Pages : 117
Book Description
This book on Newton's method is a user-oriented guide to algorithms and implementation. In just over 100 pages, it shows, via algorithms in pseudocode, in MATLAB, and with several examples, how one can choose an appropriate Newton-type method for a given problem, diagnose problems, and write an efficient solver or apply one written by others. It contains trouble-shooting guides to the major algorithms, their most common failure modes, and the likely causes of failure. It also includes many worked-out examples (available on the SIAM website) in pseudocode and a collection of MATLAB codes, allowing readers to experiment with the algorithms easily and implement them in other languages.
Publisher: SIAM
ISBN: 9780898718898
Category : Mathematics
Languages : en
Pages : 117
Book Description
This book on Newton's method is a user-oriented guide to algorithms and implementation. In just over 100 pages, it shows, via algorithms in pseudocode, in MATLAB, and with several examples, how one can choose an appropriate Newton-type method for a given problem, diagnose problems, and write an efficient solver or apply one written by others. It contains trouble-shooting guides to the major algorithms, their most common failure modes, and the likely causes of failure. It also includes many worked-out examples (available on the SIAM website) in pseudocode and a collection of MATLAB codes, allowing readers to experiment with the algorithms easily and implement them in other languages.
Newton's Method Applied to Two Quadratic Equations in C2 Viewed as a Global Dynamical System
Author: John H. Hubbard
Publisher: American Mathematical Soc.
ISBN: 9780821866320
Category : Mathematics
Languages : en
Pages : 162
Book Description
Introduction Fundamental properties of Newton maps Invariant 3-manifolds associated to invariant circles The behavior at infinity when $a=b=0$ The Farey blow-up The compactification when $a=b=0$ The case where $a$ and $b$ are arbitrary Bibliography
Publisher: American Mathematical Soc.
ISBN: 9780821866320
Category : Mathematics
Languages : en
Pages : 162
Book Description
Introduction Fundamental properties of Newton maps Invariant 3-manifolds associated to invariant circles The behavior at infinity when $a=b=0$ The Farey blow-up The compactification when $a=b=0$ The case where $a$ and $b$ are arbitrary Bibliography
Dynamical Systems
Author: Shlomo Sternberg
Publisher: Courier Corporation
ISBN: 0486135144
Category : Mathematics
Languages : en
Pages : 276
Book Description
A pioneer in the field of dynamical systems discusses one-dimensional dynamics, differential equations, random walks, iterated function systems, symbolic dynamics, and Markov chains. Supplementary materials include PowerPoint slides and MATLAB exercises. 2010 edition.
Publisher: Courier Corporation
ISBN: 0486135144
Category : Mathematics
Languages : en
Pages : 276
Book Description
A pioneer in the field of dynamical systems discusses one-dimensional dynamics, differential equations, random walks, iterated function systems, symbolic dynamics, and Markov chains. Supplementary materials include PowerPoint slides and MATLAB exercises. 2010 edition.