Rigorous numerical models for the dynamics of complex Hénon mappings on their chain recurrent sets

Discrete and Continuous Dynamical Systems

Volumn 15, Issue 2, 2006, Pages 529-558

  Hruska, Suzanne Lynch ^a  

^a INDIANA UNIVERSITY   (United States)

Author keywords

Complex dynamics; H non maps; Pseudotrajectories; Recurrence; Rigorous numerics

Indexed keywords

EID: 33745307341     PISSN: 10780947     EISSN: None     Source Type: Journal    
DOI: 10.3934/dcds.2006.15.529     Document Type: Article

References (24)

1. Dynamics at Cornell. [http://www.math.cornell.edu/~dynamics].
2. 2: currents, equilibrium measure and hyperbolicity. Invent. Math., 103(1):69-99, 1991.
3. 2. II. Stable manifolds and recurrence. J. Amer. Math. Soc., 4(4):657-679, 1991.
4. Interval Computations, [http://www.cs.utep.edu/interval-comp/].
5. T. Cormen et al. Introduction to Algorithms. The MIT Electrical Engineering and Computer Science Series. The MIT Press and McGraw-Hill Book Company, 1990.
6. M. Dellnitz and A. Hohmann. A subdivision algorithm for the computation of unstable manifolds and global attractors. Numer. Math., 75(3):293-317, 1997.
7. M. Dellnitz and O. Junge. Set oriented numerical methods for dynamical systems. In Handbook of dynamical systems, Vol. 8, pages 221-264. North-Holland, Amsterdam, 2002.
8. M. Eidenschink. Exploring Global Dynamics: A Numerical Algorithm Based on the Conley Index Theory. PhD thesis, Georgia Institute of Technology, 1995.
9. S. Friedland and J. Milnor. Dynamical properties of plane polynomial automorphisms. Ergodic Theory Dynamical Systems, 9(1):67-99, 1989.
10. J.S.L. Hruska. On the numerical construction of hyperbolic structures for complex dynamical systems. PhD thesis, Cornell University, 2002. Available for download at the Stony Brook Dynamical Systems Thesis Server [http://www.math. sunysb.edu/dynamics/theses/index.html].
11. S. L. Hruska. A numerical method for constructing the hyperbolic structure of complex Hénon mappings, to appear, preprint available at [http://xxx.arxiv.org]. Foundations of Computational Mathematics.
12. S.L. Hruska. Constructing an expanding metric for dynamical systems in one complex variable. Nonlinearity, 18:81-100, 2005.
13. J. Hubbard and K. Papadantonakis. Exploring the parameter space of complex Hénon mappings. Journal of Experimental Mathematics, to appear.
14. J.H. Hubbard and R.W. Oberste-Vorth, Hénon mappings in the complex domain. II. projective and inductive limits of polynomials. In B. Branner and P. Hjorth, editors, Real and Complex Dynamical Systems, volume 464 of NATO Adv. Sci. Inst. Ser. C Math. Phys. Sci., pages 89-132. Kluwer Acad. Publ., Dordrecht, 1995.
15. K. Mischaikow. Topological techniques for efficient rigorous computations in dynamics. Acta Numerica, 11:435-477, 2002.
16. R.E. Moore. Interval Analysis. Prentice-Hall, Englewood Cliffs, New Jersey, 1966.
17. R.E. Moore. Methods and Applications of Interval Analysis. SIAM Studies in Applied Mathematics, Philadelphia, 1979.
18. R. Oliva. On the combinatorics of external rays in the dynamics of the complex Hénon map. PhD thesis, Cornell University, 1998.
19. G. Osipenko. On the symbolic image of a dynamical system. In Boundary value problems (Russian), pages 101-105, 198. Perm. Politekh. Inst., Perm', 1983.
20. G. Osipenko. Construction of attractors and filtrations. In Conley index theory (Warsaw, 1997), volume 47 of Banach Center Publ., pages 173-192. Polish Acad. Sci., Warsaw, 1999.
21. G. Osipenko and S. Campbell. Applied symbolic dynamics: attractors and filtrations. Discrete Contin. Dynam. Systems, 5(1):43-60, 1999.
22. PROFIL/BIAS Interval Arithmetic Package. [http://www.ti3.tu-harburg.de/ Software/PROFILEnglisch.html].
23. 2. Ergodic Theory Dynam. Systems, 10(4):823-827, 1990.
24. W. Tucker. A rigorous ODE solver and Smale's 14th problem. Found. Comput. Math., 2(1):53-117, 2002.