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Fractional iteration of functions of two variables

1970
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Bulletin of the Australian Mathematical Society
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Let X € {R 2 , C 2 } and T • «i = h v1 x k y l , Vl = lb v1 x k y l (fc, Z » 0 , k+l > l ) be an invertible holomorphic function from a neighbourhood of 0 € if to ? 10 ? 0 1 the linear part of T . In this thesis, 010 b 01 ) the fractional iteration of T is examined when (1) X = C 2 , * = [ j 0] , 0 < |»| 5 |a| < 1 , (2) X = C 2 , A = [« i] , 0 < |a| < 1 , (3) X = R 2 , X = f° j] , b 2 < ha , 0 < a < 1 , (10 x = R 2 . A-In the first three cases the fractional iterates are obtained from the

doi:10.1017/s000497270004171x
fatcat:tpljhxvxbzbsjks7uapypdlzau