Dynamics Reported

1. Front Matter

   Pages I-IX

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2. The “Spectral” Decomposition for One-Dimensional Maps

   • Alexander M. Blokh

   Pages 1-59

3. A Constructive Theory of Lagrangian Tori and Computer-assisted Applications

   • Alessandra Celletti, Luigi Chierchia

   Pages 60-129

4. Ergodicity in Hamiltonian Systems

   • Carlangelo Liverani, Maciej P. Wojtkowski

   Pages 130-202

5. Linearization of Random Dynamical Systems

   • Thomas Wanner

   Pages 203-268

DYNAMICS REPORTED reports on recent developments in dynamical systems. Dynamical systems of course originated from ordinary differential equations. Today, dynamical systems cover a much larger area, including dynamical processes described by functional and integral equations, by partial and stochastic differential equations, etc. Dynamical systems have involved remarkably in recent years. A wealth of new phenomena, new ideas and new techniques are proving to be of considerable interest to scientists in rather different fields. It is not surprising that thousands of publications on the theory itself and on its various applications are appearing DYNAMICS REPORTED presents carefully written articles on major subjects in dy­ namical systems and their applications, addressed not only to specialists but also to a broader range of readers including graduate students. Topics are advanced, while detailed exposition of ideas, restriction to typical results - rather than the most general one- and, last but not least, lucid proofs help to gain the utmost degree of clarity. It is hoped, that DYNAMICS REPORTED will be useful for those entering the field and will stimulate an exchange of ideas among those working in dynamical systems Summer 1991 Christopher K. R. T Jones Drs Kirchgraber Hans-Otto Walther Managing Editors Table of Contents The "Spectral" Decomposition for One-Dimensional Maps Alexander M. Blokh Introduction and Main Results 1. 1 Preliminaries . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1. 0. 1. 1. Historical Remarks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 1. 2. A Short Description of the Approach Presented . . . . . . . . . . .. . . . . . . . . . . . . . . 3 1. 3. Solenoidal Sets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 Basic Sets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1. 4.

• Ergodizität
• Hamiltonian
• Hypothese
• Parameter
• Power
• Rang
• analytic function
• convergence
• dynamical system
• dynamical systems
• ergodicity
• hamiltonian system
• invariant
• manifold
• random dynamical system

• Division of Applied Mathematics, Brown University, Providence, Rhode Island, USA

  C. K. R. T. Jones

• Mathematics Swiss Federal Institute of Technology (ETH), Zürich, Switzerland

  U. Kirchgraber

• Mathematics Ludwig-Maximilians University, Munich, Germany

  H. O. Walther

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