Nonlinear dynamics: Quantizing the classical cat

  title={Nonlinear dynamics: Quantizing the classical cat},
  author={I. N. Stewart},
A mathematical analysis of a pendulum system reveals the relevance to quantum systems of the classical concept of ‘monodromy’ — why a falling cat always lands the right way up. 

Integrable systems, symmetries, and quantization

These notes are an expanded version of a mini-course given at the Poisson 2016 conference in Geneva. Starting from classical integrable systems in the sense of Liouville, we explore the notion of

Nearly-integrable perturbations of the Lagrange top : applications of KAM-theory

Motivated by the Lagrange top coupled to an oscillator, we consider the quasi-periodic Hamiltonian Hopf bifurcation. To this end, we develop the normal linear stability theory of an invariant torus

The quasi-periodic Hamiltonian Hopf bifurcation

We consider the quasi-periodic dynamics of non-integrable perturbations of a family of integrable Hamiltonian systems with normally 1 : −1 resonant invariant tori. In particular, we focus on the

A novel smooth and discontinuous oscillator with strong irrational nonlinearities

In this paper, we propose a novel nonlinear oscillator with strong irrational nonlinearities having smooth and discontinuous characteristics depending on the values of a smoothness parameter. The

Symplectic theory of completely integrable Hamiltonian systems

This paper explains the recent developments on the symplectic theory of Hamiltonian completely integrable systems on symplectic 4-manifolds, compact or not. One fundamental ingredient of these

Living in a physical world XII. Keeping up upward and down downward

  • S. Vogel
  • Physics
    Journal of Biosciences
  • 2007
It is shown that neutral stability opens a possibility for ground-level wind dispersal – one exploited by, at least, Russian thistles (tumbleweeds) in the drier parts of North America.

Generation of Attosecond Pulses in Atoms and Molecules

In several experiments, we demonstrate the potential of the process of high-order harmonic generation for observing ultrafast intra-molecular electron and nuclear dynamics. The largest part of this