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Melody and Variation Generation Through KAM Theory

Octavio A. Agustín-Aquino, Alicia Santiago-Santos

Abstract

We use the Newton iteration of KAM theory for diffeomorphisms of the circle as a source for melody generation and its variations

Melody and Variation Generation Through KAM Theory

Abstract

We use the Newton iteration of KAM theory for diffeomorphisms of the circle as a source for melody generation and its variations
Paper Structure (5 sections, 1 theorem, 19 equations, 1 algorithm)

This paper contains 5 sections, 1 theorem, 19 equations, 1 algorithm.

Table of Contents

  1. Introduction
  2. Some basic notions
  3. Arnold's theorem
  4. Algorithm and implementation details
  5. Some examples

Key Result

theorem thmcountertheorem

If then there is an $N$ such that the change of variables $H=H_{1}\circ\cdots\circ H_{N}$ is analytical and conjugates $\phi$ to $R_{\rho}$.

Theorems & Definitions (3)

  • definition thmcounterdefinition
  • definition thmcounterdefinition
  • theorem thmcountertheorem: Arnold, 1965, Arnold2009