Isentropic real cubic maps

International Journal of Bifurcation and Chaos in Applied Sciences and Engineering

Volumn 13, Issue 7, 2003, Pages 1701-1709

  Martins, Nuno ^a   Severino, Ricardo ^b   Sousa Ramos, J ^b  

^a INSTITUTO SUPERIOR TÉCNICO   (Portugal)

^b UNIVERSITY OF MINHO   (Portugal)

Author keywords

General symbolic dynamics; Maps of the interval; Topological dynamics

Indexed keywords

COMBINATORIAL MATHEMATICS; ENTROPY; MAPPING; MODAL ANALYSIS;

TOPOLOGICAL ENTROPY;

TOPOLOGY;

EID: 0141618398     PISSN: 02181274     EISSN: None     Source Type: Journal    
DOI: 10.1142/S0218127403007552     Document Type: Conference Paper

References (10)

1. Almeida, P., Lampreia, J. P. & Sousa Ramos, J. [1996] "Topological invariants for bimodal maps," European Conf. Iteration Theory, Batschuns, 1992 (World Scientific, Singapore), pp. 1-8.
2. Douady, A. & Hubbard, J. [1984, 1995] "Etude dynamique des polynômes quadratiques complexes I & II," Plub. Mat. d'Orsay.
3. Douady, A. [1995] "Topological entropy of unimodal maps: Monotonicity for quadratic polynomials," in Real and Complex Dynamical Systems, eds. Branner, B. & Hjorth, P. (Kluwer, Dordrecht), pp. 1-8.
4. Guckenheimer, J. [1979] "Sensitive dependence on initial conditions for one dimensional dynamics," Commun. Math. Phys. 70, 173-160.
5. Lampreia, J. P., Severino, R. & Sousa Ramos, J. [1999] "Renormalizations for cubic maps," ECIT, Annales Mathematicae Silesianae 13, 193-204.
6. MacKay, R. & C. Tresser, C. [1988] "Boundary of chaos for bimodal maps of the interval," J. London Math. Soc. 37, 164-181.
7. Milnor, J. & Thurston, W. [1988] "On iterated maps of the interval," in Dynamical Systems: Proc. Univ. Maryland 1986-1987, Lecture Notes in Mathematics, Vol. 1342 (Springer, Berlin, NY), pp. 465-563.
8. Milnor, J. & Tresser, C. [2000] "On entropy and monotonicity for real cubic maps," Commun. Math. Phys. 209, 123-178.
9. Severino, R. [2000] "Invariantes topológicos e algébricos em sistemas dinâmicos discretos," Ph.D. Thesis, Universidade Técnica de Lisboa.
10. Skjolding, H., Branner-Jorgensen, B., Christiansen, P. & Jensen, H. [1983] "Bifurcations in discrete dynamical systems with cubic maps," SIAM J. Appl. Math. 43, 520-534.