By Michael F. Barnsley, Stephen G. Demko
1986 1st Ed. Vol. 2 educational Press
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Additional resources for Chaotic Dynamics and Fractals
Actually, this process can This plane is tiled not only under reflection by a single square but also under translation by the larger fundamental square containing squares 1, 2, 3, and 4. Thus, if we translate all the larger fundamental squares containing line segments back upon the lower left fundamental square, our straight line billiard orbit has been reduced to the funda mental square shown in Fig. 5. Because of periodicity under translation, the top and bottom sides of this fundamental square are identical as are the left and right sides.
D. Cohen (North-Holland, Amsterdam, 1980). 3. V. M. Alekseev and M. V. Yakobson, "Symbolic Dynamics and Hyperbolic Dynamical Systems," Physics Reports 75, 287 (1981). 4. Gregory J. Chaitin, "Godel's Theorem and Information," Intl. d. Theor. Phys. 22_9 941 (1982). 5. " Physics Today 36, #4, 40 (1983). 6. " in The New Physics, Edited by S. Capelin and P. Davies (Cambridge University Press, Cambridge, 1986). 7. Bruno Eckhardt, Joseph Ford, and Franco Vivaldi, "Analyti cally Solvable Dynamical Systems Which Are Not Integrable," Physica 13D, 339 (1984).
46 (Am. Inst. , New York, 1978). 2. Robert H. G. Helleman, "Self-Generated Chaotic Behavior in Nonlinear Mechanics," in Fundamental Problems in Statistical Mechanics, Vol. 5, Edited by E. G. D. Cohen (North-Holland, Amsterdam, 1980). 3. V. M. Alekseev and M. V. Yakobson, "Symbolic Dynamics and Hyperbolic Dynamical Systems," Physics Reports 75, 287 (1981). 4. Gregory J. Chaitin, "Godel's Theorem and Information," Intl. d. Theor. Phys. 22_9 941 (1982). 5. " Physics Today 36, #4, 40 (1983). 6. " in The New Physics, Edited by S.
Chaotic Dynamics and Fractals by Michael F. Barnsley, Stephen G. Demko