## Point mapping stability |

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### Contents

Fundamentals on point mappings | 1 |

Critical cases | 9 |

Calculation of | 30 |

Copyright | |

6 other sections not shown

### Common terms and phrases

absolute value analytic approximating mapping area preserving mappings asymptotically stable autonomous behaviour calculations change of variables chapter corresponding cosw critical defined degree approximation determined difference equations differential equations dimensional discrete trajectories domain double point dt2 dt equa equilibrium point example exp(-jT expressions fixed point origin formal differential system given Hamiltonian Systems higher degree terms homoclinic points initial conditions integer invariant curves passing invariant directions iterates ja.h Jacobian Let us consider limit cycles linear change Lyapunov function mapping associated matrix method mn mn mn multipliers equal neighbourhood node numerical integration obtained order cycle order point mapping osculation parameters parametric resonance periodic coefficients piecewise constant point or cycle pointwise transformation real multipliers recurrent equations respect saddle points saddle type second degree terms separatrices series expansions sign definite singularities sinw solutions stable unstable stochastic third degree terms tions vector written