4 citations · 4 across the 1 of their papers we have counts for
10 papers
Spectral properties of renormalization for area-preserving maps
Denis Gaidashev, Tomas Johnson
Area-preserving maps have been observed to undergo a universal period-doubling cascade, analogous to the famous Feigenbaum-Coullet-Tresser period doubling cascade in one-dimensiona…
Rigidity for infinitely renormalizable area-preserving maps
Denis Gaidashev, Tomas Johnson, Marco Martens
The period doubling Cantor sets of strongly dissipative Henon-like maps with different average Jacobian are not smoothly conjugated. The Jacobian Rigidity Conjecture says that the…
Rigorous Enclosures of a Slow Manifold
John Guckenheimer, Tomas Johnson, Philipp Meerkamp
Slow-fast dynamical systems have two time scales and an explicit parameter representing the ratio of these time scales. Locally invariant slow manifolds along which motion occurs o…
A numerical study of infinitely renormalizable area-preserving maps
Denis Gaidashev, Tomas Johnson
It has been shown in (Gaidashev et al, 2010) and (Gaidashev et al, 2011) that infinitely renormalizable area-preserving maps admit invariant Cantor sets with a maximal Lyapunov exp…
No elliptic islands for the universal area-preserving map
Tomas Johnson
A renormalization approach has been used in \cite{EKW1} and \cite{EKW2} to prove the existence of a \textit{universal area-preserving map}, a map with hyperbolic orbits of all bina…
Dynamics of the Universal Area-Preserving Map Associated with Period Doubling: Stable Sets
Denis Gaidashev, Tomas Johnson
It is known that the famous Feigenbaum-Coullet-Tresser period doubling universality has a counterpart for area-preserving maps of ${\fR}^2$. A renormalization approach has been use…