# Linear vs nonlinear and infinite vs finite: An interpretation of chaos

## Abstract

An example of a linear infinite-dimensional system is presented that exhibits deterministic chaos and thus challenges the presumably unquestionable connection between chaos and nonlinearity. Via this example, the roles of, and relationships between, linearity, nonlinearity, infinity and finiteness in the occurrence of chaos are investigated. The analysis of these complementary but related aspects leads to: a new interpretation of chaos as the manifestation of incompressible and thus incompressible information and a conjecture about the nonexistence of operationally accessible linear systems.

- Authors:

- Publication Date:

- Research Org.:
- Oak Ridge National Lab., TN (USA)

- Sponsoring Org.:
- DOE/ER

- OSTI Identifier:
- 6502672

- Report Number(s):
- ORNL/TM-11667

ON: DE91002522

- DOE Contract Number:
- AC05-84OR21400

- Resource Type:
- Technical Report

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 99 GENERAL AND MISCELLANEOUS//MATHEMATICS, COMPUTING, AND INFORMATION SCIENCE; RANDOMNESS; STATISTICAL MODELS; DYNAMICS; NONLINEAR PROBLEMS; MATHEMATICAL MODELS; MECHANICS; 990200* - Mathematics & Computers

### Citation Formats

```
Protopopescu, V.
```*Linear vs nonlinear and infinite vs finite: An interpretation of chaos*. United States: N. p., 1990.
Web. doi:10.2172/6502672.

```
Protopopescu, V.
```*Linear vs nonlinear and infinite vs finite: An interpretation of chaos*. United States. doi:10.2172/6502672.

```
Protopopescu, V. Mon .
"Linear vs nonlinear and infinite vs finite: An interpretation of chaos". United States.
doi:10.2172/6502672. https://www.osti.gov/servlets/purl/6502672.
```

```
@article{osti_6502672,
```

title = {Linear vs nonlinear and infinite vs finite: An interpretation of chaos},

author = {Protopopescu, V.},

abstractNote = {An example of a linear infinite-dimensional system is presented that exhibits deterministic chaos and thus challenges the presumably unquestionable connection between chaos and nonlinearity. Via this example, the roles of, and relationships between, linearity, nonlinearity, infinity and finiteness in the occurrence of chaos are investigated. The analysis of these complementary but related aspects leads to: a new interpretation of chaos as the manifestation of incompressible and thus incompressible information and a conjecture about the nonexistence of operationally accessible linear systems.},

doi = {10.2172/6502672},

journal = {},

number = ,

volume = ,

place = {United States},

year = {Mon Oct 01 00:00:00 EDT 1990},

month = {Mon Oct 01 00:00:00 EDT 1990}

}

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