Geometrical approach for description of the mixed state in multi-well potentials

• Main Authors: Berezovoj, V.P., Bolotin, Yu.L., Ivashkevych, G.I.
• Format: Article
• Language: English
• Published: Національний науковий центр «Харківський фізико-технічний інститут» НАН України 2007
• Series: Вопросы атомной науки и техники
• Subjects: Nonlinear dynamics
• Online Access: http://dspace.nbuv.gov.ua/handle/123456789/110968

We use the so-called geometrical approach [1] in description of transition from regular motion to chaotic one in Hamiltonian systems with potential energy surface that has several local minima. Distinctive feature of such systems is coexistence of different types of dynamics (regular or chaotic) in different wells at the same energy [2]. Application of traditional criteria for transition to chaos (resonance overlap criterion, negative curvature criterion and stochastic layer destruction criterion) is inefficient in case of potentials with complex topology. Geometrical approach allows considering only configuration space but not phase space when investigating the stability. In this approach all information about chaos and regularity is contained in potential function. The aim of this work is to determine what details of geometry of potential lead to chaos in Hamiltonian systems using geometrical approach. Numerical calculations are executed for potentials that are relevant with lowest umbilical catastrophes.