arXiv subjects

K. Fuchss

Publications and source records attributed to K. Fuchss.

3 recordsLinked to original sources

arXiv2006

On a new fixed point of the renormalization group operator for area-preserving maps

The breakup of the shearless invariant torus with winding number $ω=\sqrt{2}-1$ is studied numerically using Greene's residue criterion in the standard nontwist map. The residue behavior and parameter scaling at the breakup suggests the existence of a new fixed point of the renormalization group operator (RGO) for area-preserving maps. The unstable eigenvalues of the RGO at this fixed point and the critical scaling exponents of the torus at breakup are computed.

nlin.CD↗

arXiv2006

Breakup of Shearless Meanders and "Outer" Tori in the Standard Nontwist Map

The breakup of shearless invariant tori with winding number $ω=[0,1,11,1,1,...]$ (in continued fraction representation) of the standard nontwist map is studied numerically using Greene's residue criterion. Tori of this winding number can assume the shape of meanders (folded-over invariant tori which are not graphs over the x-axis in $(x,y)$ phase space), whose breakup is the first point of focus here. Secondly, multiple shearless orbits of this winding number can exist, leading to a new type of breakup scenario. Results are discussed within the framework of the renormalization group for area-preserving maps. Regularity of the critical tori is also investigated.

nlin.CD↗

arXiv2004

Meanders and Reconnection-Collision Sequences in the Standard Nontwist Map

New global periodic orbit collision/separatrix reconnection scenarios in the standard nontwist map in different regions of parameter space are described in detail, including exact methods for determining reconnection thresholds that are implemented numerically. The results are compared to a break-up diagram of shearless invariant curves. The existence of meanders (invariant tori that are not graphs) is demonstrated numerically for both odd and even period reconnection for certain regions in parameter space, and some of the implications on transport are discussed.

nlin.CD↗