Nonlinear Perron–Frobenius Theory by Bas Lemmens
In the past several decades the classical Perron-Frobenius theory for nonnegative matrices has been extended to obtain remarkably precise and beautiful results for classes of nonlinear maps. This nonlinear Perron-Frobenius theory has found significant uses in computer science, mathematical biology, game theory and the study of dynamical systems. This is the first comprehensive and unified introduction to nonlinear Perron-Frobenius theory suitable for graduate students and researchers entering the field for the first time. It acquaints the reader with recent developments and provides a guide to challenging open problems. To enhance accessibility, the focus is on finite dimensional nonlinear Perron-Frobenius theory, but pointers are provided to infinite dimensional results. Prerequisites are little more than basic real analysis and topology.-
The Geometry of Fractal Sets
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Riemannian Geometry
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Miniquaternion Geometry
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The Geometry of Total Curvature on Complete Open Surfaces
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Metric Spaces
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Birational Geometry and Manin's Conjecture
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Coherence in Three-Dimensional Category Theory
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Dilation and Model Theory for Pairs of Commuting Contraction Operators
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The Direct Method in Soliton Theory
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Matrix Positivity
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Rigidity in Higher Rank Abelian Group Actions: Volume 1, Introduction and Cocycle Problem
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Topics in Critical Point Theory
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Category and Measure
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The Mathieu Groups
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Modern Approaches to the Invariant-Subspace Problem
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Frobenius Manifolds and Moduli Spaces for Singularities
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Group Cohomology and Algebraic Cycles
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Permutation Group Algorithms
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Abelian Varieties, Theta Functions and the Fourier Transform
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Matrices of Sign-Solvable Linear Systems
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The Cube-A Window to Convex and Discrete Geometry
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The Large Sieve and its Applications
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Combinatorics of Minuscule Representations
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Polynomials and Vanishing Cycles
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Restricted Orbit Equivalence for Actions of Discrete Amenable Groups
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Metric Diophantine Approximation on Manifolds
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Applications of Diophantine Approximation to Integral Points and Transcendence
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An Introduction to Homotopy Theory
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Linear and Projective Representations of Symmetric Groups
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Dependence with Complete Connections and its Applications
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Fixed Point Theory and Applications
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Justification Logic
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Synthetic Geometry of Manifolds
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Dynamical Systems and Semisimple Groups
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Distribution Modulo One and Diophantine Approximation
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The Levy Laplacian
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Sets of Multiples
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Period Domains over Finite and p-adic Fields
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Large Deviations for Markov Chains
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Levy Processes in Lie Groups
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Character Sums with Exponential Functions and their Applications
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Poincare Duality Algebras, Macaulay's Dual Systems, and Steenrod Operations
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Quasi-Frobenius Rings
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The Covering Property Axiom, CPA
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Ridge Functions
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Jordan Structures in Geometry and Analysis
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Typical Dynamics of Volume Preserving Homeomorphisms
'In their introduction the authors state that 'the main purpose of this book is to give a systematic self-contained introduction to nonlinear Perron–Frobenius theory and to provide a guide to various challenging open problems'They have achieved their aim excellently.' Hans Schneider, University of Wisconsin, Madison
'Undoubtedly, this remarkable book will be of interest to all specialists in nonlinear analysis and its applications. Certainly, any mathematical library ought to carry this book.' Peter Zabreiko, Zentralblatt MATH
'This textbook is a carefully arranged journey through large parts of this beautiful theory, which has seen various contributions by the authors in the past. The material is accessible with little more than a basic knowledge of linear algebra, real analysis and some topology. The book is self-contained, all results are proven very rigorously, and where appropriate, the evolution of results is explained and framed in the historical context. I recommend this book very warmly and without any reservations to anyone interested in nonlinear Perron–Frobenius theory.' Bjorn S. Ruffer, Mathematical Reviews
'Undoubtedly, this remarkable book will be of interest to all specialists in nonlinear analysis and its applications. Certainly, any mathematical library ought to carry this book.' Peter Zabreiko, Zentralblatt MATH
'This textbook is a carefully arranged journey through large parts of this beautiful theory, which has seen various contributions by the authors in the past. The material is accessible with little more than a basic knowledge of linear algebra, real analysis and some topology. The book is self-contained, all results are proven very rigorously, and where appropriate, the evolution of results is explained and framed in the historical context. I recommend this book very warmly and without any reservations to anyone interested in nonlinear Perron–Frobenius theory.' Bjorn S. Ruffer, Mathematical Reviews
Bas Lemmens is a Lecturer in Mathematics at the University of Kent, Canterbury. His research interests lie in nonlinear operator theory, dynamical systems theory and metric geometry. He is one of the key developers of nonlinear Perron–Frobenius theory. Roger Nussbaum is a Professor of Mathematics at Rutgers University. His research interests include nonlinear differential-delay equations, the theory of nonlinear positive operators and fixed point theory and its applications. He has published extensively on nonlinear Perron–Frobenius theory.
| SKU | Unavailable |
| ISBN 13 | 9780521898812 |
| ISBN 10 | 0521898811 |
| Title | Nonlinear Perron–Frobenius Theory |
| Author | Bas Lemmens |
| Series | Cambridge Tracts In Mathematics |
| Condition | Unavailable |
| Binding Type | Hardback |
| Publisher | Cambridge University Press |
| Year published | 2012-05-03 |
| Number of pages | 336 |
| Cover note | Book picture is for illustrative purposes only, actual binding, cover or edition may vary. |
| Note | Unavailable |