Zeros of the kneading invariant and topological entropy for Lorenz maps

Nonlinearity

Volumn 9, Issue 4, 1996, Pages 999-1014

  Glendinning, Paul ^a,c   Hall, Toby ^b,d  

^a DAMTP   (United Kingdom)

^b INSTITUT D ESTUDIS CATALANS   (Spain)

^c QUEEN MARY UNIVERSITY OF LONDON   (United Kingdom)

^d UNIVERSITY OF LIVERPOOL   (United Kingdom)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0141519849     PISSN: 09517715     EISSN: None     Source Type: Journal    
DOI: 10.1088/0951-7715/9/4/010     Document Type: Article

References (19)

1. Alsedà L and Llibre J 1989 Kneading theory of Lorenz maps Dyn. Syst. and Erg. Thy., Banach Centre Publ. 23 83
2. Alsedà L, Llibre J, Mañosas F and Misiurewicz M 1988 Lower bounds of the topological entropy for continuous maps of the circle of degree one Nonlinearity 1 463
3. Alsedà L, Llibre J, Misiurewicz M and Tresser C 1989 Periods and entropy for Lorenz-like maps Ann. Inst. Fourier, Grenoble 39 929
4. Alsedà L and Mañosas F 1990 Kneading theory and rotation intervals for a class of circle maps of degree one Nonlinearity 3 413
5. Arnéodo A, Coullet P and Tresser C 1981 A possible new mechanism for the onset of turbulence Phys. Lett. A 81 197
6. Block L S, Guckenheimer J, Misiurewicz M and Young L-S 1980 Periodic points and topological entropy of one-dimensional maps Lecture Notes in Mathematics 819 (Berlin: Springer)
7. de Melo W and van Strien S 1993 One-Dimensional Dynamics (Berlin: Springer)
8. Gambaudo J-M, Procaccia I, Thomae S and Tresser C 1987 New universal scenarios for the onset of chaos in Lorenz-type flows Phys. Rev. Lett. 57 925-928
9. Glendinning P and Sparrow C 1993 Prime and renormalisable kneading invariants and the dynamics of expanding Lorenz maps Physica D 62 22-50
10. Guckenheimer J and Williams R F 1979 Structural stability of Lorenz attractors Publ. Math. I.H.E.S. 50 59-72
11. Hubbard J H and Sparrow C T 1990 The classification of topologically expanding Lorenz maps Comm. Pure. Appl. Math. 43 431-443
12. Jonker L and Rand D A 1981 Bifurcations in one dimension I. The non-wandering set Inv. Math. 62 347-365
13. Malkin M I 1991 Rotation intervals and the dynamics of Lorenz type mappings Selecta Math. Sov. 10 265-275
14. Milnor J and Thurston W 1988 On iterated maps of the interval Lecture Notes in Mathematics 1342 (Berlin: Springer)
15. Misiurewicz M and Szlenk W 1980 Entropy of piecewise monotone mappings Studia Math. 67 45-63
16. Rand D A 1978 The topological classification of Lorenz attractors Math. Proc. Camb. Phil Soc. 83 451-460
17. van Strien S 1981 On the bifurcations creating horseshoes Lecture Notes in Mathematics 898 (Berlin: Springer)
18. van Strien S 1988 Smooth dynamics on the interval in New directions in dynamical systems eds. T Bedford and J Swift LMS Lecture Notes Series 127 (Cambridge: Cambridge University Press)
19. Williams R F 1979 The structure of Lorenz attractors Publ. Math. IHES 50 73-99