Using chaos to shadow the quadratic map for all time

References

• Armbruster , D. , Nicolaenko , B. , Smaoui , N. and Chossat , P. 1996 . Symmetries and dynamics for the 2-D Navier-Stokes flow . Physica D , 95 : 81 – 93 .
   Google Scholar
• Smaoui , N. and Armbruster , D. 1997 . Symmetries and the Karhunén-loeve analysis . SIAM Journal on Scientific Computing , 18 ( 5 )
   Web of Science ®Google Scholar
• Smaoui , N. and Aladwani , S. 1997 . Using artificial neural network to model chaotic time series of ethernet traffic . Journal of Mathematical Modelling and Scientific Computing , 8
   Google Scholar
• Kostelich , E.J. , Grebogi , C. , Ott , E. and Yorke , J.A. 1993 . Higher-dimensional targeting . Physical Rev.E , 47 ( 1 )
   Web of Science ®Google Scholar
• Shinbrot , T. , Ott , E. , Grebogi , C. and Yorke , J.A. 1992 . Using chaos to direct orbits to targets in systems describable by a one-dimensional map . Physical Rev. A , 45 ( 6 )
   PubMed Web of Science ®Google Scholar
• Shinbrot , T. , Ott , E. , Grebogi , C. and Yorke , J.A. 1990 . Using chaos to direct trajectories to targets . Physical Rev. Lett. , 65 ( 26 )
   PubMed Web of Science ®Google Scholar
• Grebogi , C. , Kostelich , E. , Ott , E. and Yorke , J.A. 1986 . Multi-dimensioned interwined basin boundaries and the kicked double rotor . Phys. Lett. A , 118 ( 9 )
   Web of Science ®Google Scholar
• Grebogi , C. , Kostelich , E. , Ott , E. and Yorke , J.A. 1987 . Multi-dimensioned interwined basin boundaries:Basin structure of the kicked double rotor . Physica D , 25 ( 9 ) : 347 – 360 .
   Google Scholar
• Kostelich , E. and Yorke , J.A. 1987 . Lorenz cross sections of the chaotic attractor of the double rotor . Physica D , 24 ( 9 ) : 263 – 278 .
   Google Scholar
• Hammel , S. , Yorke , J. and Grebogy , C. 1987 . Do Numerical Orbits of Chaotic Dynamical Processes Represent True Orbits? . Journal of Complexity , 3 ( 9 ) : 136 – 145 .
   Google Scholar
• Hammel , S. , Yorke , J. and Grebogy , C. October 1988 . “ Numerical Orbits of Chaotic Processes Represent True Orbits ” . In Bulletin (New Series) of the American Mathematical Society Vol. 19 , October ,
   Google Scholar
• Sauer , T. and Yorke , J.A. 1990 . Rigorous verification of trajectories for the computer simulation of dynamical system Preprint
   Google Scholar
• Krebs , C.J. The experimental Analysis of Distribution and Abundance , New York : Harper and Row .
   Google Scholar
• Strogatz , S.H. Nonlinear Dynamics and Chaos:With applications to physics, biology,chemistry and engineering , Addison-Wesley .
   Google Scholar
• Anosov , D.V. 1967 . Geodesic flows and closed Riemannian manifolds with negative curvature . Proc. Steklov Inst. Math , 90
   Google Scholar
• Bowen , R. 1975 . w-limit sets for Axiom A diffeomorphisms . J. Differential Equations , 18
   Google Scholar
• Coven , E.M. , Kan , I. and Yorke , J.A. 1988 . Pseudo-orbit shadowing in the family of tent maps . Transactions of the American Mathematical Society , 308 ( 1 )
   Web of Science ®Google Scholar
• Nusse , H.E. and Yorke , J.A. Is Every Approximate Trajectory of some Process Near an Exact Trajectory of a Nearby Process? Preprint
   Google Scholar