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A GLUING LEMMA FOR ITERATED FUNCTION SYSTEMS
, 2015We obtain a special version of gluing lemma related to the theory of iterated function systems (IFS). As an application, we verify that a family of concrete n-dimensional self-affine tiles {Tn, r : 0 ≤ r < 3, n ≥ 3} are homeomorphic with the unit cube [0,
T. Kamae, J. Luo, Bo Tan
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1992
Publisher Summary This chapter discusses iterative functions. The simplest way to experiment with mathematical chaos is to use something called an iterative function. A linear equation gives rise to a straight line, and does not give any chaotic behavior.
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Publisher Summary This chapter discusses iterative functions. The simplest way to experiment with mathematical chaos is to use something called an iterative function. A linear equation gives rise to a straight line, and does not give any chaotic behavior.
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On the iterates of Euler's function
Archiv der Mathematik, 2001Asymptotic representations are given for the three sums \(\textstyle\sum\limits \limits _{n\le x} \varphi (n)/\varphi \bigl (\varphi (n)\bigr )\), \(\textstyle\sum\limits \limits _{n\le x} \varphi (n)/\varphi \bigl (\varphi (n)\bigr )\), \(\textstyle\sum\limits \limits _{n\le x}\ \log \, \varphi (n)/\varphi \bigl (\varphi (n)\bigr )\ ; \ \varphi\) is ...
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On the iteration of rational functions
Mathematical Proceedings of the Cambridge Philosophical Society, 1978In the theory of the iteration of a rational function or transcendental entire function R(z) of the complex variable z we study the sequence of natural iterates, {Rn(z):n = 0, 1,…}, of R, whereThe domain of definition of the iterates is , the extended complex plane (if R is rational), and (if R is entire transcendental) with the topology of the ...
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Cyclic iterated function systems
Journal of Fixed Point Theory and Applications, 2020R. Pasupathi, A. Chand, M. Navascués
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Ergodic Shadowing Properties of Iterated Function Systems
Bulletin of the Malaysian Mathematical Sciences Society, 2020Huoyun Wang, Q. Liu
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Iteration of Rational Functions
The American Mathematical Monthly, 1991Alan F. Beardon, Robert L. Devaney
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Hardy–Rogers Type Iterated Function Systems
, 2020Flavian Georgescu +2 more
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