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It is known that the kneading matrix associated with a continuous piecewise monotone self-map of an interval contains crucial combinatorial information of the map and all its iterates, however for every iterate of such a map we can associate its kneading matrix. In this paper, we describe the relation between kneading matrices of maps and their iterates for a family of chaotic maps. We also give a new definition for the kneading matrix and describe the relationship between the corresponding determinant and the usual kneading determinant of such maps.
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참고문헌 (11)
참고문헌 신청
J. F. Alves / 2004 / Kneading theory for tree maps / Ergodic Theory Dynam. Systems 24(4):957~985
V. Baladi / 1995 / Infinite kneading matrices and weighted zeta functions of interval maps / J. Funct. Anal 128(1):226~244
R. L. Devaney / 2003 / An Introduction to Chaotic Dynamical Systems, Studies in Nonlinearity / Westview Press
R. A. Holmgren / 1994 / A First Course in Discrete Dynamical Systems, Universitext / SpringerVerlag
D. A. Mendes / 2004 / Kneading theory for triangular maps / Int. J. Pure Appl. Math 10(4):421~450
V. Baladi / 1995 / Infinite kneading matrices and weighted zeta functions of interval maps / J. Funct. Anal 128(1):226~244
R. L. Devaney / 2003 / An Introduction to Chaotic Dynamical Systems, Studies in Nonlinearity / Westview Press
R. A. Holmgren / 1994 / A First Course in Discrete Dynamical Systems, Universitext / SpringerVerlag
D. A. Mendes / 2004 / Kneading theory for triangular maps / Int. J. Pure Appl. Math 10(4):421~450
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