Analytical solutions to one-dimensional dissipative and discrete chaotic dynamics

被引：4
作者：
Pingel, D
Schmelcher, P
Diakonos, FK
机构：
[1] Univ Heidelberg, Inst Phys Chem, D-69120 Heidelberg, Germany
[2] Univ Athens, Dept Phys, GR-15771 Athens, Greece
来源：
PHYSICAL REVIEW E | 1998年 / 58卷 / 01期
关键词：
D O I：
10.1103/PhysRevE.58.369
中图分类号：
O35 [流体力学]; O53 [等离子体物理学];
学科分类号：
070204 ; 080103 ; 080704 ;
摘要：
Analytical solutions to the chaotic and ergodic motion of a certain class of one-dimensional dissipative and discrete dynamical systems are derived. This allows us to obtain exact expressions for physical properties such as the time correlation function. We illustrate our solutions by means of a few examples for which conventional numerical trajectory calculations fail to predict the correct behavior.
引用
收藏
页码：369 / 375
页数：7
相关论文
共 12 条
[1]  
Bender C.M., 1978, Advanced mathematical methods for scientists and engineers
[2]  
CAULEY JL, 1994, CAMBRIDGE NONLINEAR, V2
[3]   OBSTRUCTIONS TO SHADOWING WHEN A LYAPUNOV EXPONENT FLUCTUATES ABOUT ZERO [J].
DAWSON, S ;
GREBOGI, C ;
SAUER, T ;
YORKE, JA .
PHYSICAL REVIEW LETTERS, 1994, 73 (14) :1927-1930
[4]   On the construction of one-dimensional iterative maps from the invariant density: The dynamical route to the beta distribution [J].
Diakonos, FK ;
Schmelcher, P .
PHYSICS LETTERS A, 1996, 211 (04) :199-203
[5]   SHADOWING OF PHYSICAL TRAJECTORIES IN CHAOTIC DYNAMICS - CONTAINMENT AND REFINEMENT [J].
GREBOGI, C ;
HAMMEL, SM ;
YORKE, JA ;
SAUER, T .
PHYSICAL REVIEW LETTERS, 1990, 65 (13) :1527-1530
[6]   FULLY-DEVELOPED CHAOTIC 1-D MAPS [J].
GYORGYI, G ;
SZEPFALUSY, P .
ZEITSCHRIFT FUR PHYSIK B-CONDENSED MATTER, 1984, 55 (02) :179-186
[7]   PROPERTIES OF FULLY-DEVELOPED CHAOS IN ONE-DIMENSIONAL MAPS [J].
GYORGYI, G ;
SZEPFALUSY, P .
JOURNAL OF STATISTICAL PHYSICS, 1984, 34 (3-4) :451-475
[8]   TIME-CORRELATION FUNCTIONS OF ONE-DIMENSIONAL TRANSFORMATIONS [J].
MORI, H ;
SO, BC ;
OSE, T .
PROGRESS OF THEORETICAL PHYSICS, 1981, 66 (04) :1266-1283
[9]  
Pincherle S., 1920, RENDICONTI REALE ACA, V29, P329
[10]   Analytical solution of the logistic equation [J].
Rabinovich, S ;
Berkolaiko, G ;
Buldyrev, S ;
Shehter, A ;
Havlin, S .
INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS, 1997, 7 (04) :837-838
12