Complexity, fractal dimensions and topological entropy in dynamical systems. (English) Zbl 1136.37320
Collet, P. (ed.) et al., Chaotic dynamics and transport in classical and quantum systems. Proceedings of the NATO Advanced Study Institute and international summer school, Cargèse, Corsica, France, 18–30 August, 2003. Dordrecht: Springer (ISBN 1-4020-2946-2/pbk; 1-4020-2945-4/hbk; 1-4020-2947-0/e-book). NATO Science Series II: Mathematics, Physics and Chemistry 182, 35-72 (2005).
Summary: Instability of orbits in dynamical systems is the reason for their complex behavior. Main characteristics of this complexity are \(\varepsilon\)-complexity, topological entropy and fractal dimension. In this two lectures we give a short introduction to ideas, results and machinery of this part of modern nonlinear dynamics.
For the entire collection see [Zbl 1078.37002].
For the entire collection see [Zbl 1078.37002].
MSC:
| 37C45 | Dimension theory of smooth dynamical systems |
| 28A80 | Fractals |
| 37B40 | Topological entropy |
| 37D45 | Strange attractors, chaotic dynamics of systems with hyperbolic behavior |
| 37B10 | Symbolic dynamics |
| 37B20 | Notions of recurrence and recurrent behavior in topological dynamical systems |
| 37B25 | Stability of topological dynamical systems |
