Iterative Functional Equations

Front Cover
Cambridge University Press, Jul 27, 1990 - Mathematics - 552 pages
0 Reviews
A cohesive and comprehensive account of the modern theory of iterative functional equations. Many of the results included have appeared before only in research literature, making this an essential volume for all those working in functional equations and in such areas as dynamical systems and chaos, to which the theory is closely related. The authors introduce the reader to the theory and then explore the most recent developments and general results. Fundamental notions such as the existence and uniqueness of solutions to the equations are stressed throughout, as are applications of the theory to such areas as branching processes, differential equations, ergodic theory, functional analysis and geometry. Other topics covered include systems of linear and nonlinear equations of finite and infinite ORD various function classes, conjugate and commutable functions, linearization, iterative roots of functions, and special functional equations.
  

What people are saying - Write a review

We haven't found any reviews in the usual places.

Contents

Introduction
1
2B Clockgraduation and the concept of chronon
9
LIB Limit points of the sequence of iterates
15
2B Analytic mappings
22
3D Special cases
30
5A Generalizations of the Banach contraction principle
37
Linear equations and branching processes
51
2A Negative g
60
6A Continuous and differentiable solutions
259
Equations of infinite order and systems of nonlinear equations
270
2B Important special case
279
2E Denumerabie order
285
4B Approximation in Bucks sense
293
5B Important special case
301
6C Differentiable solutions of hsystems
307
6E Integrable solutions of hsystems
308

3D An example
66
4C A difference equation
72
5C Special inhomogeneous equation
78
6C Restricted stationary measures
86
Regularity of solutions of linear equations
96
functions
106
3C Asymptotic series expansions
115
5B Julias equation
124
6B Homogeneous equation
132
IB Doubly stochastic measures supported on a hairpin
138
Analytic and integrable solutions of linear equations
148
2B Existence and uniqueness results
152
3C General homogeneous and inhomogeneous equations
159
6B The Abel equation
168
7C Homogeneous equation
174
Theory of nonlinear equations
185
2D Existence via solutions of inequalities
192
3D Comparison with the linear case
199
5JB Lipschitzian Nemytskii operators
206
6C Lack of uniqueness of C solutions
214
8A Existence and uniqueness of Lp solutions
222
8D U solution depending on an arbitrary function
228
Equations of higher orders and systems of linear equations
235
2B Decomposition of twoplace functions
243
4B Real solutions when some characteristic roots of g
249
5C Solution depending on an arbitrary function
255
8A A crucial inequality
320
On conjugacy
332
2C Further results on smooth solutions
339
5A Julias equation and the iterative logarithm
346
7B Convergence of formal power series having iterative logarithm
357
More on the Schroder and Abel equations
365
Characterization of functions
389
2B Exponential functions
395
3C Sine
403
4B Riemannintegrable solutions of an auxiliary equation
409
5A The Weierstrass c n d functions
414
Iterative roots and invariant curves
421
1I 2C Strictly decreasing roots of strictly increasing functions
427
AD Convex and concave iterative roots
436
5C Uniqueness conditions
442
6D Fractional iterates of the roots of identity function
449
8B Volkmann s theorem
457
9C Lack of uniqueness of Lipschitzian solutions
463
2A Comparison theorems
475
12AB Regular solution
483
5B Properties of solutions of the inequality
489
7B A property of the particular solution
497
References
504
Author index
546
Copyright

Common terms and phrases

References to this book

All Book Search results »

Bibliographic information