The book employs oscillatory dynamical systems to represent the Universe mathematically via constructing classical and quantum theory of damped oscillators. It further discusses isotropic and homogeneous metrics in the Friedman-Robertson-Walker Universe and shows their equivalence to non-stationary oscillators. The wide class of exactly solvable damped oscillator models with variable parameters is associated with classical special functions of mathematical physics. Combining principles with observations in an easy to follow way, it inspires further thinking for mathematicians and physicists.

Contents

Part I: Dissipative geometry and general relativity theory

Pseudo-Riemannian geometry and general relativity

Dynamics of universe models

Anisotropic and homogeneous universe models

Metric waves in a nonstationary universe and dissipative oscillator

Bosonic and fermionic models of a Friedman–Robertson–Walker universe

Time dependent constants in an oscillatory universe

Part II: Variational principle for time dependent oscillations and dissipations

Lagrangian and Hamilton descriptions

Damped oscillator: classical and quantum theory

Sturm–Liouville problem as a damped oscillator with time dependent damping and frequency

Riccati representation of time dependent damped oscillators

Quantization of the harmonic oscillator with time dependent parameters