428 research outputs found
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
Chaotic dynamics of three-dimensional H\'enon maps that originate from a homoclinic bifurcation
We study bifurcations of a three-dimensional diffeomorphism, , that has
a quadratic homoclinic tangency to a saddle-focus fixed point with multipliers
(\lambda e^{i\vphi}, \lambda e^{-i\vphi}, \gamma), where
and . We show that in a
three-parameter family, g_{\eps}, of diffeomorphisms close to , there
exist infinitely many open regions near \eps =0 where the corresponding
normal form of the first return map to a neighborhood of a homoclinic point is
a three-dimensional H\'enon-like map. This map possesses, in some parameter
regions, a "wild-hyperbolic" Lorenz-type strange attractor. Thus, we show that
this homoclinic bifurcation leads to a strange attractor. We also discuss the
place that these three-dimensional H\'enon maps occupy in the class of
quadratic volume-preserving diffeomorphisms.Comment: laTeX, 25 pages, 6 eps figure
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
Magnetic anisotropy in strained manganite films and bicrystal junctions
Transport and magnetic properties of LSMO manganite thin films and bicrystal
junctions were investigated. Manganite films were epitaxially grown on STO,
LAO, NGO and LSAT substrates and their magnetic anisotropy were determined by
two techniques of magnetic resonance spectroscopy. Compare with cubic
substrates a small (about 0.3 persentage), the anisotropy of the orthorhombic
NGO substrate leads to a uniaxial anisotropy of the magnetic properties of the
films in the plane of the substrate. Samples with different tilt of
crystallographic basal planes of manganite as well as bicrystal junctions with
rotation of the crystallographic axes (RB - junction) and with tilting of basal
planes (TB - junction) were investigated. It was found that on vicinal NGO
substrates the value of magnetic anisotropy could be varied by changing the
substrate inclination angle from 0 to 25 degrees. Measurement of magnetic
anisotropy of manganite bicrystal junction demonstrated the presence of two
ferromagnetically ordered spin subsystems for both types of bicrystal
boundaries RB and TB. The magnitude of the magnetoresistance for TB - junctions
increased with decreasing temperature and with the misorientation angle even
misorientation of easy axes in the parts of junction does not change. Analysis
of the voltage dependencies of bicrystal junction conductivity show that the
low value of the magnetoresistance for the LSMO bicrystal junctions can be
caused by two scattering mechanisms with the spin- flip of spin - polarized
carriers due to the strong electron - electron interactions in a disordered
layer at the bicrystal boundary at low temperatures and the spin-flip by anti
ferromagnetic magnons at high temperatures.Comment: 26 pages, 10 figure
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