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Discrete Dynamics on Locally Conformal Framework

Oğul Esen, Ayten Gezici, Hasan Gümral

Abstract

In this paper, we address the globalization problem of discrete Lagrangian and Hamiltonian dynamics in locally conformal framework.

Discrete Dynamics on Locally Conformal Framework

Abstract

In this paper, we address the globalization problem of discrete Lagrangian and Hamiltonian dynamics in locally conformal framework.
Paper Structure (9 sections, 6 theorems, 98 equations)

This paper contains 9 sections, 6 theorems, 98 equations.

Table of Contents

  1. Introduction
  2. Locally Conformally Continuous Dynamics
  3. Locally Conformally Symplectic Geometry
  4. Locally Conformally Lagrangian Dynamics
  5. Locally Conformally Discrete Dynamics
  6. Discrete Lagrangian and Discrete Hamiltonian Dynamics
  7. Locally Conformally Discrete Lagrangian Dynamics
  8. Locally Conformally Discrete Hamiltonian Dynamics
  9. Conclusion and Future Work

Key Result

Proposition 3.1

The discrete Euler-Lagrange (dEL) equation, arising from a discrete Lagrangian function $L^d$, is where $D_1$ denotes the partial derivative with respect to the first argument whereas $D_2$ is the partial derivative with respect to the second argument.

Theorems & Definitions (11)

  • Proposition 3.1
  • Proof 3.2
  • Proposition 3.3
  • Proof 3.4
  • Proposition 3.5
  • Proof 3.6
  • Proposition 3.7
  • Proof 3.8
  • Proposition 3.9
  • Proof 3.10
  • ...and 1 more