The reconstruction theorem for endomorphisms

Bulletin of the Brazilian Mathematical Society

Volumn 33, Issue 2, 2002, Pages 231-262

  Takens, Floris ^a  

^a UNIVERSITY OF GRONINGEN   (Netherlands)

Author keywords

Dimension; Entropy; Generic; Read out function; Reconstruction

Indexed keywords

EID: 0036667157     PISSN: 01003569     EISSN: None     Source Type: Journal    
DOI: 10.1007/s005740200012     Document Type: Article

References (22)

1. [A] D. Aeyels, Generic observability of differentiable systems, SIAM J. Control and Optimisation, 19 (1981), 595-603.
2. [B] Th. Bröcker, Differentiable germs and catastrophes, Camb. Univ. Press, (1975).
3. [GPa] P. Grassberger, I. Procaccia, Measuring the strangeness of strange attractors, Physica 9D (1983a), 189-208.
4. [GPb] P. Grassberger, I. Procaccia, Characterisation of strange attractors, Phys. Rev. Lett. 50 (1983b), 346-349.
5. [GWPL] C.G. Gibson, K. Wirthmüller, A.A. du Plessis, E.J.N. Looijenga, Topological stability of smooth mappings, Lecture Notes in Mathematics 552, Springer-Verlag, (1976).
6. [H] M.W. Hirsch, Differential topology, Springer-Verlag, (1976).
7. [KS] H. Kantz, T. Schreiber, Nonlinear time series analysis, Cam. Univ. Press, (1997).
8. [L] S. Lojasiewiecz, Ensembles semi-analytiques, I.H.E.S., (1965).
9. [O] J.C. Oxtoby, Measure and category, Springer-Verlag, (1971).
10. [P] Ya.B. Pessin, Dimension theory in dynamical systems, University of Chicago Press, (1997).
11. [RO] C. Robinson, Dynamical systems, CRC Press, (1995).
12. [RU] D. Ruelle, Historical behaviour in smooth dynamical systems, in Global analysis of dynamical systems, ed.: H.W. Broer, B. Krauskopf and G. Vegter, IoP, (2001), 63-66.
13. [S] S. Smale, Differentiable dynamical systems, Bull. A.M.S. 73 (1967), 747-817.
14. [SYC] T. Sauer, J. A. Yorke, M. Casdagli, Embedology, J. Statistical Physics 65 (3/4) (1991), 579-616.
15. [T6] R. Thom, Un lemma sur les applications différentiables, Bol. Soc. Mat. Mex. 2 (1956), 59-71.
16. [T9] R. Thom, Ensembles et morphismes stratifiés, Bull. A.M.S., 75 (1969), 240-284.
17. [T1] F. Takens, Detecting strange attractors in turbulence, in Dynamical systems and turbulence, Warwick 1980, ed. D. A. Rand, L-S. Young, LNM 898, Springer-Verlag, (1981).
18. [T3] F. Takens, Invariants related to dimension and entropy, in: Atas do 13° colóquio bras. de mat. 1981, IMPA, Rio de Janeiro, (1983).
19. [TV] F. Takens, E. Verbitskiy, Generalised entropies: Rényi and correlation integral approach, Nonlinearity 11 (1998), 771-782.
20. [V] E.A. Verbitskiy, Generalised entropies in dynamical systems, Ph.D thesis, University of Groningen (2000).
21. [W5] H. Whitney, Differentiable manifolds, Ann. of Math. 37 (1935), 645-680.
22. [W4] H. Whitney, The self-intersections of a smooth n-manifold in 2n-space and (2n - 1)-space, Ann. of Math. 45 (1944), 220-293.