About the Book
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.
Table of Contents:
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.
