830 research outputs found
Epigroups whose subepigroup lattice is lower semimodular
We characterize epigroups mentioned in the title. © 2012 Springer Science+Business Media, LLC
On local and global aspects of the 1:4 resonance in the conservative cubic H\'enon maps
We study the 1:4 resonance for the conservative cubic H\'enon maps
with positive and negative cubic term. These maps show up
different bifurcation structures both for fixed points with eigenvalues
and for 4-periodic orbits. While for the 1:4 resonance unfolding
has the so-called Arnold degeneracy (the first Birkhoff twist coefficient
equals (in absolute value) to the first resonant term coefficient), the map
has a different type of degeneracy because the resonant term can
vanish. In the last case, non-symmetric points are created and destroyed at
pitchfork bifurcations and, as a result of global bifurcations, the 1:4
resonant chain of islands rotates by . For both maps several
bifurcations are detected and illustrated.Comment: 21 pages, 13 figure
On the hierarchy of partially invariant submodels of differential equations
It is noticed, that partially invariant solution (PIS) of differential
equations in many cases can be represented as an invariant reduction of some
PIS of the higher rank. This introduce a hierarchic structure in the set of all
PISs of a given system of differential equations. By using this structure one
can significantly decrease an amount of calculations required in enumeration of
all PISs for a given system of partially differential equations. An equivalence
of the two-step and the direct ways of construction of PISs is proved. In this
framework the complete classification of regular partially invariant solutions
of ideal MHD equations is given
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