Extensions of Minimal Transformation Groups

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.