ISSN:
1420-8903
Keywords:
Primary 39B05
Source:
Springer Online Journal Archives 1860-2000
Topics:
Mathematics
Notes:
Abstract Letf be an invertible function on the real lineR, and letZ denote the set of integers. For eachx εZ, letf |n| denote then'th iterate off. Clearlyf |m|(f |n|(x))=f |m+n|(x) for allm,nεZ and allxεR. LetG be any group of orderc, the cardinality of the continuum, which contains (an isomorphic copy of)Z as a normal subgroup. If for eachxεR, the iteration trajectory (orbit) ofx is non-periodic, then there exists a set of invertible functionsF={F |α|:αεG} on the real line with the properties (i)F |α|(F |β|(x))=F |α+β| (x) for allxεR and (ii)F |n|(x)=f |n|(x) for allnεZ andxεR. That is,f can be embedded in a set ofG-generalized iterates. In particular,f can be embedded in a set of complex generalized iterates.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/BF02189400
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