### Abstract

Scattering is a fundamental tool for probing many physical and chemical processes. In a scattering experiment, particles are injected into the system and their characteristics after the scattering are recorded, from which many properties of the system can be revealed. In a general sense, scattering can be defined as a problem of obtaining various relations between some output variables characterizing the particles after the scattering versus some input variables characterizing the particles before the scattering. The relations are called scattering functions. In a regular scattering process, the functions are typically smooth, examples of which can be found in textbooks of classical mechanics. It has been realized, however, that there can be situations in which a scattering function may contain an uncountably infinite number of singularities. Near any of the singularities, an arbitrarily small change in the input variable can cause a large change in the output variable. This is a sensitive dependence on initial conditions that signifies the appearance of chaos. Scattering in this case is chaotic.

Original language | English |
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Title of host publication | Applied Mathematical Sciences (Switzerland) |

Publisher | Springer |

Pages | 187-238 |

Number of pages | 52 |

DOIs | |

Publication status | Published - Jan 1 2011 |

### Publication series

Name | Applied Mathematical Sciences (Switzerland) |
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Volume | 173 |

ISSN (Print) | 0066-5452 |

ISSN (Electronic) | 2196-968X |

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### Keywords

- Deflection Angle
- Escape Rate
- Periodic Orbit
- Topological Entropy
- Unstable Manifold

### ASJC Scopus subject areas

- Applied Mathematics

### Cite this

*Applied Mathematical Sciences (Switzerland)*(pp. 187-238). (Applied Mathematical Sciences (Switzerland); Vol. 173). Springer. https://doi.org/10.1007/978-1-4419-6987-3_6