## Chaos, yet no chance to get lost: order and structure in the chaotic dynamical behaviour of one-dimensional noninvertible axiom a mappings, arising in discrete biological models |

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### Contents

INTRODUCTION | 1 |

Introduction for the nonspecialist and some | 7 |

Abstract of the thesis introduction | 33 |

25 other sections not shown

### Common terms and phrases

Absbound(f absorbing boundary point Aoo(f Asstaper(f Assume that f asymptotically periodic asymptotically stable fixed asymptotically stable periodic Axiom A mapping compact set conclude continuous mapping Crit(f critical point defined Definition denote direct domain domain of attraction eventually expanding expanding map f is eventually f satisfies f with period finite type fk(x fn(x following properties homeomorphism irreducible iterates Lebesgue measure zero Lemma Let f limsup mapping f mapping g Math neighbourhood non-wandering points non-wandering set nonempty compact set nonnegative integer one-sided topologically transitive open cover orbit of f orbits don,t converge permutation matrix points for f positive integer positively f-invariant set Proof restriction of f Schwarzian derivative sequence set of asymptotically set of f set of points Sf(x spectral radius stable fixed point stable periodic orbit stable periodic points strictly monotonously subset theorem topological entropy topologically conjugate union zeta function