2007/10/18 by Klaus Jaenich, Jaenich, Klaus
Mathematics · Physics and Astronomy · #21 pages #Chaotic Dynamics (nlin.CD) #Dynamical Systems (math.DS) #FOS: Mathematics #FOS: Physical sciences #LaTeX #Magnetic confinement fusion research #Quantum chaos and dynamical systems #Scientific Research and Discoveries #Symplectic Geometry (math.SG) #math.DS #math.SG #msc:21 #nlin.CD
paper · pdf · doi:10.48550/arxiv.0710.3466
arxiv created 2007/10/18 · openalex publication_date 2007/10/18 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We study a class of 2-dimensional Hamiltonian systems H(x,y,px,py)=\frac12(px2+py2) +V(x,y) in which the plane x=px=0 is invariant under the Hamiltonian flow, so that straight-line librations along the y axis exist, and we also consider perturbations δH=δ⋅ F(x,y,px,py) that preserve these librations. We describe a procedure for the analytical calculation of partial derivatives of the Poincaré map. These partial derivatives can be used to predict the bifurcation behavior of the libration, in particular to distinguish between transcritical and fork-like bifurcations, as was mathematically investigated in [1] and numerically studied in [2]. [1] K. Jänich, arXiv.org/abs/0710.3464 [2] M. Brack and K. Tanaka, arXiv:0705.0753