Discrete dynamical systems: dynamics, bifurcations and integrability

  1. Dynamics of 2-dimensional maps derived from a discrete Sine-Gordon equation.  In this work we investigate the dynamics of a two dimensional maps.  This maps is integrable, however interesting (or maybe even wild) behavior is still observed due to the presence of singularities of the map. 
  2. On a generalized Sine-Gordon ordinary difference equation.  We study the integrals of a mapping derived from the generalized Sine-Gordon equation.  We are looking for structure of these integal as the dimension of the maps increases.
  3. Chaotic dynamics in a kicked harmonic oscillator.     

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