A Geometric Approach to a Quantum Counterpart of a Saddle-Node Bifurcation in a 1:1 Resonant Perturbed Oscillator

DOI10.1142/S0218127498000759zbMath0949.37026MaRDI QIDQ4936308

Yoshio Uwano

Publication date: 25 January 2000

Published in: International Journal of Bifurcation and Chaos (Search for Journal in Brave)

zbMATH Keywords

oscillatorHamiltonian systemsbifurcation theorysaddle nodes

Mathematics Subject Classification ID

Forced motions for nonlinear problems in mechanics (70K40) Quantum chaos (81Q50) Bifurcations of singular points in dynamical systems (37G10) Perturbations of finite-dimensional Hamiltonian systems, normal forms, small divisors, KAM theory, Arnol'd diffusion (37J40)

Related Items (1)

A quantum saddle-node bifurcation in a \(1\: 1\) resonant perturbed oscillator with four parameters

Cites Work

• On resonant non linearly coupled oscillators with two equal frequencies
• Maslov's quantization conditions for the bound states of the hydrogen atom
• ON BIFURCATIONS IN THE SCHRÖDINGER PROBLEM ADMITTING OF AN EXISTENCE OF NONLINEAR SHIFT OPERATORS

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