Abstract
With the concept of fractals, introduced by B. B. Mandelbrot in the 1970s, geometry assumes again, after Poincaré, a leading role in the theory of dynamical systems and chaos. Dynamical instability and unpredictability in time become inseparable from geometrical complexity and irregularity in space, through self-similarity under scaling. Chaos theory thus acquires its natural setting and description in terms of fractal geometry and symbolic dynamics. Objects of non-integer dimension and distributions with spectra of generalized dimensions become familiar concepts of aesthetic, even philosophical value, while giving researchers at the same time new tools to probe deeper into complex natural phenomena. In this paper, I review in a pedagogical way the main ideas of fractal geometry, multifractal distributions and symbolic dynamics. Of central importance is the connection between temporal and spatial complexity, while important applications of the formalism are also mentioned, particularly in the area of chaotic time series analysis.
| Original language | English |
|---|---|
| Pages (from-to) | 281-322 |
| Number of pages | 42 |
| Journal | Open Systems and Information Dynamics |
| Volume | 4 |
| Issue number | 3 |
| Publication status | Published - 1997 |
| Externally published | Yes |
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ASJC Scopus subject areas
- Fluid Flow and Transfer Processes
- Physical and Theoretical Chemistry
- Information Systems
- Computational Mechanics
- Mechanics of Materials
- Mathematical Physics
- Statistics and Probability
- Statistical and Nonlinear Physics
Cite this
Fundamental concepts of classical chaos. Part II : Fractals and chaotic dynamics. / Bountis, Tassos.
In: Open Systems and Information Dynamics, Vol. 4, No. 3, 1997, p. 281-322.Research output: Contribution to journal › Article
}
TY - JOUR
T1 - Fundamental concepts of classical chaos. Part II
T2 - Fractals and chaotic dynamics
AU - Bountis, Tassos
PY - 1997
Y1 - 1997
N2 - With the concept of fractals, introduced by B. B. Mandelbrot in the 1970s, geometry assumes again, after Poincaré, a leading role in the theory of dynamical systems and chaos. Dynamical instability and unpredictability in time become inseparable from geometrical complexity and irregularity in space, through self-similarity under scaling. Chaos theory thus acquires its natural setting and description in terms of fractal geometry and symbolic dynamics. Objects of non-integer dimension and distributions with spectra of generalized dimensions become familiar concepts of aesthetic, even philosophical value, while giving researchers at the same time new tools to probe deeper into complex natural phenomena. In this paper, I review in a pedagogical way the main ideas of fractal geometry, multifractal distributions and symbolic dynamics. Of central importance is the connection between temporal and spatial complexity, while important applications of the formalism are also mentioned, particularly in the area of chaotic time series analysis.
AB - With the concept of fractals, introduced by B. B. Mandelbrot in the 1970s, geometry assumes again, after Poincaré, a leading role in the theory of dynamical systems and chaos. Dynamical instability and unpredictability in time become inseparable from geometrical complexity and irregularity in space, through self-similarity under scaling. Chaos theory thus acquires its natural setting and description in terms of fractal geometry and symbolic dynamics. Objects of non-integer dimension and distributions with spectra of generalized dimensions become familiar concepts of aesthetic, even philosophical value, while giving researchers at the same time new tools to probe deeper into complex natural phenomena. In this paper, I review in a pedagogical way the main ideas of fractal geometry, multifractal distributions and symbolic dynamics. Of central importance is the connection between temporal and spatial complexity, while important applications of the formalism are also mentioned, particularly in the area of chaotic time series analysis.
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UR - http://www.scopus.com/inward/citedby.url?scp=3042970880&partnerID=8YFLogxK
M3 - Article
AN - SCOPUS:3042970880
VL - 4
SP - 281
EP - 322
JO - Open Systems and Information Dynamics
JF - Open Systems and Information Dynamics
SN - 1230-1612
IS - 3
ER -