Extensions of Minimal Transformation Groups

ISBN-13: 9789028603684 / Angielski / Twarda / 1979 / 320 str.

I. U. Bronstein

Opis

This edition is an almost exact translation of the original Russian text. A few improvements have been made in the present ation. The list of references has been enlarged to include some papers published more recently, and the latter are marked with an asterisk. THE AUTHOR vii LIST OF SYMBOLS M = M(X, T, rr. ) 1,3. 3 A(X, T) 2.7. 3 M(R) 2.9. 4 2 C (Y, T, p), G, h] 3.16. 6 P = P(X, T, rr. ) 3,16. 12 1'3. 3 C9v (Y, T, p), G, h] Px 2.8. 9 E = E(X, T, rr. ) 1,4. 7 Q = Q(X, T, rr. ) 1,3. 3 3,12. 8 Ey Q" = Q" (X, T, rr. ) = Q#(X, T, rr. ) Ext (Y, T, p), G, h] 3,16. 4 Ext9v (Y, T, p), G, h] 3,16. 12 2.8. 31 Q" (R) = Q#(R) 3.13. 5 3,12. 12 Gy 3,15. 4 Sx(A) 2,8. 18 G(X, Y) SeA) 2.8. 22 2 3,16. 8 H cY, T, rr. ), G, h] HE, (X, T, rr. ) = (X, T) 3'12. 12 1'1. 1 Y (X, T, rr., G, a) 4.21. 4 3'16. 1 Hef) HK(f) 4.21. 9 H(X, T) 2,7. 3 1- 3,19. 1 L = L(X, T, rr. ) 1,3. 3 viii I NTRODUCTI ON 1. It is well known that an autonomous system of ordinary dif ferential equations satisfying conditions that ensure uniqueness and extendibility of solutions determines a flow, i. e. a one parameter transformation group. G. D."

Spis treści

I Topological Transformation Groups.- 1.1 Basic Definitions.- 1.2 Recursion.- 1.3 Relations.- 1.4 The Ellis Semigroup.- 1.5 Pointwise Almost Periodic Transformation Groups.- 1.6 Distal and Equicontinuous Transformation Groups.- II Minimal Transformation Groups.- 2.7 The Enveloping Semigroup Of a Minimal Transformation Group.- 2.8 Almost Periodic and Locally almost periodic minimal sets.- 2.9 Distal Minimal Transformation Groups.- 2.10 Transitive Distal Transformation Groups and Nil-Flows.- 2.11 Topological Properties of Minimal Sets.- III Extensions of Minimal Transformation Groups.- 3.12 The basic Theory of Extensions.- 3.13 Equicontinuous and Stable Extensions.- 3.14 The Structure of Distal and Almost Distal Extensions.- 3.15 Groups Associated with Minimal Extensions.- 3.16 Group Extensions.- 3.17 Relationships Between Group Extensions and Equicontinuous Extensions; A Strengthened Structure Theorem for Distal Extensions.- 3.18 A Method for Constructing Minimal Sets.- 3.19 Disjointness.- IV Extensions and Equations.- 4.20 Shift Dynamical Systems.- 4.21 Extensions Associated with Certain Classes of Equations.- 4.22 Almost Automorphic Extensions and Synchronous Solutions of Differential Equations.- 4.23 Extensions with Zero-Dimensional Fibers and Almost Periodic Solutions.- 4.24 Linear extensions of Dynamical Systems and Linear Differential Equations.