KNEADING PLANE OF THE CIRCLE MAP

The kneading plane spanned by the pair of kneading sequences for maps of a circle to itself is the parameter space directly reflecting the dynamics. The structure of the kneading plane is analysed, a method for construction of the kneading plane proposed, and the constructed kneading plane shown.

[1]  P. Coullet,et al.  Transition to turbulence for doubly periodic flows , 1980 .

[2]  R. Pérez,et al.  Fine Structure of Phase Locking , 1982 .

[3]  Philip Boyland,et al.  Bifurcations of circle maps: Arnol'd tongues, bistability and rotation intervals , 1986 .

[4]  Floris Takens,et al.  Bifurcations and stability of families of diffeomorphisms , 1983 .

[5]  S. Shenker,et al.  Quasiperiodicity in dissipative systems: A renormalization group analysis , 1983 .

[6]  Robert S. MacKay,et al.  Some flesh on the skeleton: The bifurcation structure of bimodal maps , 1987 .

[7]  Chris Bernhardt.  Rotation Intervals of a Class of Endomorphisms of the Circle , 1982 .

[8]  J. Eckmann,et al.  Iterated maps on the interval as dynamical systems , 1980 .

[9]  Seunghwan Kim,et al.  Renormalization of Quasiperiodic Mappings , 1985 .

[10]  Wei-mou Zheng.  SYMBOLIC DYNAMICS FOR THE CIRCLE MAP , 1991 .

[11]  W. Thurston,et al.  On iterated maps of the interval , 1988 .

[12]  R. MacKay,et al.  Transition to topological chaos for circle maps , 1996 .

[13]  Leon Glass,et al.  Bistability, period doubling bifurcations and chaos in a periodically forced oscillator , 1982 .

[14]  Ryuichi Ito.  Rotation sets are closed , 1981, Mathematical Proceedings of the Cambridge Philosophical Society.

[15]  Tomas Bohr,et al.  Transition to chaos by interaction of resonances in dissipative systems. I: Circle maps , 1984 .

[16]  R. Pérez,et al.  Bifurcation and chaos in a periodically stimulated cardiac oscillator , 1983 .

[17]  Bernard Derrida,et al.  Iteration of endomorphisms on the real axis and representation of numbers , 1978 .

[18]  Nicholas C. Metropolis,et al.  On Finite Limit Sets for Transformations on the Unit Interval , 1973, J. Comb. Theory A.

[19]  J. Keener,et al.  Phase locking of biological clocks , 1982, Journal of mathematical biology.

[20]  Zheng.  Applied symbolic dynamics for the Lorenz-like map. , 1990, Physical review. A, Atomic, molecular, and optical physics.

[21]  On the Energy Transport in Linear Chains , 1974 .