# Oscillation, Rotation, and Wandering of Solutions to Linear Differential Systems

## Abstract

For solutions of a linear system on the semi-axis, we introduce a series of Lyapunov exponents that describe the oscillation, rotation, and wandering properties of these solutions. In the case of systems with constant matrices, these exponents are closely related to the imaginary parts of the eigenvalues. We examine the problem on the existence of a similar relationship in the case of piecewise constant of arbitrary systems.

- Authors:

- M. V. Lomonosov Moscow State University (Russian Federation)

- Publication Date:

- OSTI Identifier:
- 22771269

- Resource Type:
- Journal Article

- Journal Name:
- Journal of Mathematical Sciences

- Additional Journal Information:
- Journal Volume: 230; Journal Issue: 5; Conference: International symposium on differential equations, Perm (Russian Federation), 17-18 May 2016; Other Information: Copyright (c) 2018 Springer Science+Business Media, LLC, part of Springer Nature; http://www.springer-ny.com; Country of input: International Atomic Energy Agency (IAEA); Journal ID: ISSN 1072-3374

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 97 MATHEMATICAL METHODS AND COMPUTING; DIFFERENTIAL EQUATIONS; EIGENVALUES; LYAPUNOV METHOD; MATHEMATICAL SOLUTIONS; MATRICES; OSCILLATIONS; ROTATION

### Citation Formats

```
Sergeev, I. N., E-mail: igniserg@gmail.com.
```*Oscillation, Rotation, and Wandering of Solutions to Linear Differential Systems*. United States: N. p., 2018.
Web. doi:10.1007/S10958-018-3787-Z.

```
Sergeev, I. N., E-mail: igniserg@gmail.com.
```*Oscillation, Rotation, and Wandering of Solutions to Linear Differential Systems*. United States. doi:10.1007/S10958-018-3787-Z.

```
Sergeev, I. N., E-mail: igniserg@gmail.com. Tue .
"Oscillation, Rotation, and Wandering of Solutions to Linear Differential Systems". United States. doi:10.1007/S10958-018-3787-Z.
```

```
@article{osti_22771269,
```

title = {Oscillation, Rotation, and Wandering of Solutions to Linear Differential Systems},

author = {Sergeev, I. N., E-mail: igniserg@gmail.com},

abstractNote = {For solutions of a linear system on the semi-axis, we introduce a series of Lyapunov exponents that describe the oscillation, rotation, and wandering properties of these solutions. In the case of systems with constant matrices, these exponents are closely related to the imaginary parts of the eigenvalues. We examine the problem on the existence of a similar relationship in the case of piecewise constant of arbitrary systems.},

doi = {10.1007/S10958-018-3787-Z},

journal = {Journal of Mathematical Sciences},

issn = {1072-3374},

number = 5,

volume = 230,

place = {United States},

year = {2018},

month = {5}

}

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