Stability of order: An example of horseshoes "near" a linear map

International Journal of Bifurcation and Chaos in Applied Sciences and Engineering

Volumn 9, Issue 10, 1999, Pages 2081-2090

  Bollt, Erik M ^a  

^a UNITED STATES NAVAL ACADEMY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0039444522     PISSN: 02181274     EISSN: None     Source Type: Journal    
DOI: 10.1142/S0218127499001516     Document Type: Article

References (20)

1. Bollt, E. M. & Kostelich, E. J. [1998] "Optimal targeting of chaos," Phys. Lett. A245(5), 399-406.
2. Bollt, E. M. & Meiss, J. D. [1995] "Targeting chaotic orbits to the moon through recurrence," Physica D81, 280-294.
3. Chen, G. & Dong, X. [1998] From Chaos to Order. Perspectives, Methodologies, and Applications (World Scientific, Singapore).
4. Chen, G. & Lai, D. [1997] "Anticontrol of chaos via feedback," Proc. IEEE Conf. Decis. Contr., San Diego, CA, pp. 367-372.
5. Devaney, R. L. [1989] An Introduction to Chaotic Dynamical Systems, 2nd edition (Addison-Wesley, Redwood City, CA).
6. Golub, G. & van Loan, C. [1989] Matrix Computations, 2nd edition (Johns Hopkins University Press, Baltimore, MD).
7. Hirsch, M. & Smale, S. [1974] Differential Equations, Dynamical Systems and Linear Algebra (Academic Press, NY).
8. Kapitaniak, T. [1996] Controlling Chaos, Theoretical and Practical Methods in Nonlinear Dynamics (Academic Press Harcourt Brace and Company, Publishers NY).
9. Katok, A. & Hasselblatt, B. [1995] Introduction to the Modern Theory of Dynamical Systems (Cambridge University Press, Cambridge, UK).
10. Kostelich, E. J., Grebogi, C., Ott, E. & Yorke, J. A. [1993] "Higher-dimensional targeting," Phys. Rev. E47, 305-310.
11. Martelli, M., Dong, M. & Seph, T. [1998] "Defining chaos," Math. Mag. 71(2), 112-122.
12. Ogata, K. [1990] Control Engineering, 2nd edition (Prentice-Hall, Englewood, NJ), pp. 782-784.
13. Ott, E. [1994] Chaos in Dynamical Systems (Cambridge University Press, NY).
14. Ott, E., Grebogi, C. & Yorke, J. A. [1990] "Contolling chaotic dynamical systems," Chaos: Soviet-American Perspective on Nonlinear Science (American Institute of Physics, NY), pp. 153-172.
15. Ottino, J. M. [1989] The Kinematics of Mixing: Stretching, Chaos, and Transport (Cambridge University Press, NY).
16. Schiff, S. J., Jerger, K., Duong, D. H., Chang, T., Spano, M. L. & Ditto, W. L. [1994] "Controlling chaos in the brain," Nature 370, 615-620.
17. Schweizer, J. & Kennedy, M. P. [1995] Phys. Rev. E52, 4865-4876.
18. Shinbrot, T., Grebogi, C., Ott, E. & Yorke, J. A. [1993] "Using small perturbations to control chaos," Nature 363, 411-417.
19. Smale, S. [1963] "Diffeomorphisms with many periodic points," in Differential and Combinatorial Topology, ed. Cairns, S. S. (Princeton University Press, Princeton).
20. Wiggins, S. [1992] Chaotic Transport in Dynamical Systems (Springer-Verlag, NY).