Hampton Amanda E, Meiss James D
Department of Applied Mathematics, University of Colorado Boulder, Boulder, Colorado 80309-0526, USA.
Chaos. 2022 Nov;32(11):113127. doi: 10.1063/5.0103436.
We study dynamics of a generic quadratic diffeomorphism, a 3D generalization of the planar Hénon map. Focusing on the dissipative, orientation preserving case, we give a comprehensive parameter study of codimension-one and two bifurcations. Periodic orbits, born at resonant, Neimark-Sacker bifurcations, give rise to Arnold tongues in parameter space. Aperiodic attractors include invariant circles and chaotic orbits; these are distinguished by rotation number and Lyapunov exponents. Chaotic orbits include Hénon-like and Lorenz-like attractors, which can arise from period-doubling cascades, and those born from the destruction of invariant circles. The latter lie on paraboloids near the local unstable manifold of a fixed point.
我们研究一般二次微分同胚的动力学，它是平面亨农映射的三维推广。聚焦于耗散、保定向的情形，我们对余维数为一和二的分岔进行了全面的参数研究。在共振的奈马克 - 萨克分岔处产生的周期轨道在参数空间中形成阿诺德舌。非周期吸引子包括不变圆和混沌轨道；这些通过旋转数和李雅普诺夫指数来区分。混沌轨道包括类亨农和类洛伦兹吸引子，它们可由倍周期级联产生，也可由不变圆的破坏产生。后者位于定点局部不稳定流形附近的抛物面上。
