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Iterated Maps on the Interval as Dynamical Systems
Abstract
Iterations of continuous maps of an interval to itself serve as the simplest examples of models for dynamical systems. These models present an interesting mathematical structure going far beyond the simple equilibrium solutions one might expect. If, in addition, the dynamical system depends on an experimentally controllable parameter, there is a corresponding mathematical structure revealing a great deal about interrelations between the behavior for different parameter values. This work explains some of the early results of this theory to mathematicians and theoretical physicists, with the add
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Cited by
Pattern formation outside of equilibrium
Cross, M. C., & Hohenberg, P. C. (1993) · Reviews of Modern Physics · doi:10.1103/revmodphys.65.851 · Cited by 7,859
Ergodic theory of chaos and strange attractors
Eckmann, J. P., & Ruelle, D. (1985) · Reviews of Modern Physics · doi:10.1103/revmodphys.57.617 · Cited by 4,941
Self-citationPermutation Entropy: A Natural Complexity Measure for Time Series
Bandt, C., & Pompe, B. (2002) · Physical Review Letters · doi:10.1103/physrevlett.88.174102 · Cited by 4,867
Milnor, J. (1985) · Communications in Mathematical Physics · doi:10.1007/bf01212280 · Cited by 971
Coexistence of two types on a single resource in discrete time
Adler, F. R. (1990) · Journal of Mathematical Biology · doi:10.1007/bf00160232 · Cited by 29
Metadata
- Authors
- Collet, P., & Eckmann, J.-P.
- Venue
- Birkhäuser Boston eBooks
- Publisher
- Birkhäuser Boston
- Published
- 2009
- OpenAlex
- W1573241742
- Cited by
- 1,647
- References
- 0
- FWCI
- 14.43
- Type
- book
- Language
- en
- Open access
- closed
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