References

1

P. Billingsley. Ergodic Theory and Information. Wiley, New York, 1965.

2

G. D. Birkhoff. Sur quelques courbes fermées remarquables. Bull. Soc. Math. France, 60:1--26, 1932.

3

L. Block, J. Guckenheimer, M. Misiurewicz, and L. Young. Periodic points and topological entropy of one dimensional maps. In Global Theory of Dynamical Systems, volume 819 of Springer Lecture Notes in Mathematics, pages 18--34. Springer-Verlag, 1979.

4

J. M. Borwein and P. B. Borwein. Pi and the AGM: A Study in Analytic Number Theory and Computational Complexity. Wiley, New York, 1987.

5

B. A. Cipra. Computer-drawn pictures stalk the wild trajectory. Science, 241:1162--1163, 1988.

6

Robert M. Corless, Gregory W. Frank, and J. Graham Monroe. Chaos and continued fractions. Physica D, 46:241--253, 1990.

7

R. L. Devaney. An Introduction to Chaotic Dynamical Systems. Benjamin/Cummings, Menlo Park, 1985.

8

W. Gautschi. Efficient computation of the complex error function. SIAM J. Numer. Anal., 7(1):187--198, 1970.

9

J. Guckenheimer and P. Holmes. Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields. Springer-Verlag, New York, 1983.

10

G. H. Hardy and E. M. Wright. An Introduction to the Theory of Numbers. Oxford University Press, 5th edition, 1979.

11

Peter Henrici. Applied and Computational Complex Analysis, volume 2. Wiley, New York, 1977.

12

K. Ikeda and M .Mizuno. Frustrated instabilities in nonlinear optical resonators. Phys. Rev. Letters, 53(14):1340--1343, 1984.

13

W. B. Jones and W. J. Thron. Continued Fractions: Analytic Theory and Applications. Addison-Wesley, Reading, 1980.

14

A. Y. Khintchin. Continued Fractions. P. Noordhoff, Groningen, 1963.

15

T. Y. Li and J. A. Yorke. Period three implies chaos. Amer. Math. Monthly, 82:985--992, 1975.

16

R. Mañé. Ergodic Theory and Differentiable Dynamics. Springer-Verlag, Berlin, 1987.

17

I. Niven. Irrational Numbers, volume 11 of Carus Mathematical Monograph Series. MAA, New Jersey, 1956.

18

C. D. Olds. Continued Fractions. Random House, Toronto, 1963.

19

V. I. Osledec. A multiplicative ergodic theorem: Liapunov characteristic numbers for dynamical systems. Trans. Moscow Math. Soc., 19:197--231, 1968.

20

H. Poincaré. Les Méthodes Nouvelles de la Mecanique Céleste. Gauthier-Villars, 1899.

21

A. N. Saarkovskii. Coexistence of cycles of a continuous map of a line into itself. Ukr. Math. Z., 16:61--71, 1964.

22

M. R. Schroeder. Number Thoery in Science and Communication. Springer-Verlag, Berlin, 1984.

23

H. M. Stark. An explanation of some exotic continued fractions found by brillhart. In A. O. L. Atkin and B. J. Birch, editors, Computers in Number Theory (Proc. Science Research Council Atlas Symposium #2, Oxford), pages 21--35. Academic Press, 1971.

24

P. Stefan. A theorem of saarkovskii on the existence of periodic orbits of continuous endomorphisms of the real line. Comm. Math. Phys., 54:237--248, 1977.

25

S. Ushiki. Central difference scheme and chaos. Physica D, 4:407--424, 1982.

26

M. Yamaguti and S. Ushiki. Chaos in numerical analysis of ordinary differential equations. Physica D, 3(3):618--626, 1981.