TY - JOUR
T1 - Linear parabolic maps on the torus
AU - Zyczkowski, Karol
AU - Nishikawa, Takashi
N1 - Funding Information:
We are indebted to P. Ashwin for many valuable remarks and his constant interest in the progress of this work. We also thank M. Arjunwadkar, U. Feudel, C. Grebogi, J. Meiss, E. Ott, J. Stark, M. Woitkowski and J. Yorke for helpful discussions and are grateful to the anonymous referee for the several useful comments. K.Ż. acknowledges the Fulbright Fellowship and a support by the Polish KBN grant no. P03B 060 13.
PY - 1999
Y1 - 1999
N2 - We investigate linear parabolic maps on the torus. In a generic case these maps are non-invertible and discontinuous. Although the metric entropy of these systems is equal to zero, their dynamics is non-trivial due to folding of the image of the unit square into the torus. We study the structure of the maximal invariant set, and in a generic case we prove the sensitive dependence on the initial conditions. We study the decay of correlations and the diffusion in the corresponding system on the plane. We also demonstrate how the rationality of the real numbers defining the map influences the dynamical properties of the system.
AB - We investigate linear parabolic maps on the torus. In a generic case these maps are non-invertible and discontinuous. Although the metric entropy of these systems is equal to zero, their dynamics is non-trivial due to folding of the image of the unit square into the torus. We study the structure of the maximal invariant set, and in a generic case we prove the sensitive dependence on the initial conditions. We study the decay of correlations and the diffusion in the corresponding system on the plane. We also demonstrate how the rationality of the real numbers defining the map influences the dynamical properties of the system.
KW - Decay of correlations
KW - Diffusion
KW - Parabolic maps on the torus
KW - Sensitive dependence on initial conditions
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U2 - 10.1016/S0375-9601(99)00465-X
DO - 10.1016/S0375-9601(99)00465-X
M3 - Article
AN - SCOPUS:0000039071
SN - 0375-9601
VL - 259
SP - 377
EP - 386
JO - Physics Letters, Section A: General, Atomic and Solid State Physics
JF - Physics Letters, Section A: General, Atomic and Solid State Physics
IS - 5
ER -