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Nonregular languages in the kicked rotor

Binder1, Pedraza

  • 1Departamento de Fisica, Universidad de Los Andes, Apartado Aereo 4976, Bogota, Colombia.

Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics
|December 2, 2000
PubMed
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A new symbolic dynamics model for the kicked rotor (standard map) reveals distinct trajectory behaviors. These trajectories map to context-free and context-sensitive languages, offering insights into complex system dynamics.

Area of Science:

  • Physics
  • Dynamical Systems
  • Computer Science

Background:

  • The kicked rotor, a classic model in nonlinear dynamics, exhibits complex behavior, particularly in sticky regions near resonant orbits.
  • Understanding the long-term trajectories of such systems is crucial for characterizing their chaotic and regular dynamics.
  • Symbolic dynamics offers a powerful framework for analyzing the qualitative behavior of dynamical systems.

Purpose of the Study:

  • To develop a symbolic dynamics model for analyzing trajectories of the kicked rotor (standard map) in sticky regions.
  • To investigate the linguistic properties of these trajectories and their relationship to formal language theory.

Main Methods:

  • Development of a Markov chain model to represent the symbolic dynamics of kicked rotor trajectories.

Related Experiment Videos

  • Analysis of trajectory sets to determine their correspondence with formal language classes.
  • Application of concepts from automata theory and formal languages.

    • Main Results:

    • A novel symbolic dynamics framework was successfully developed for the kicked rotor model.
    • Two distinct sets of trajectories were identified within the sticky regions.
    • These trajectory sets were shown to correspond to context-free and context-sensitive languages, respectively.

    Conclusions:

    • The symbolic dynamics approach provides a new lens for understanding the complexity of kicked rotor dynamics.
    • The discovered linguistic properties of trajectories offer a novel characterization of system behavior near resonances.
    • This work bridges concepts from dynamical systems and theoretical computer science, opening avenues for further interdisciplinary research.