164 research outputs found
Topological monodromy as an obstruction to Hamiltonization of nonholonomic systems: pro or contra?
The phenomenon of a topological monodromy in integrable Hamiltonian and
nonholonomic systems is discussed. An efficient method for computing and
visualizing the monodromy is developed. The comparative analysis of the
topological monodromy is given for the rolling ellipsoid of revolution problem
in two cases, namely, on a smooth and on a rough plane. The first of these
systems is Hamiltonian, the second is nonholonomic. We show that, from the
viewpoint of monodromy, there is no difference between the two systems, and
thus disprove the conjecture by Cushman and Duistermaat stating that the
topological monodromy gives a topological obstruction for Hamiltonization of
the rolling ellipsoid of revolution on a rough plane.Comment: 31 pages, 11 figure
Hyperchaotic attractors of three-dimensional maps and scenarios of their appearance
We study bifurcation mechanisms of the appearance of hyperchaotic attractors
in three-dimensional maps. We consider, in some sense, the simplest cases when
such attractors are homoclinic, i.e. they contain only one saddle fixed point
and entirely its unstable manifold. We assume that this manifold is
two-dimensional, which gives, formally, a possibility to obtain two positive
Lyapunov exponents for typical orbits on the attractor (hyperchaos). For
realization of this possibility, we propose several bifurcation scenarios of
the onset of homoclinic hyperchaos that include cascades of both supercritical
period-doubling bifurcations with saddle periodic orbits and supercritical
Neimark-Sacker bifurcations with stable periodic orbits, as well as various
combinations of these cascades. In the paper, these scenarios are illustrated
by an example of three-dimensional Mir\'a map.Comment: 40 pages, 24 figure
Topological monodromy as an obstruction to Hamiltonization of nonholonomic systems: pro or contra?
The phenomenon of a topological monodromy in integrable Hamiltonian and nonholonomic systems is discussed. An efficient method for
computing and visualizing the monodromy is developed. The comparative
analysis of the topological monodromy is given for the rolling ellipsoid of
revolution problem in two cases, namely, on a smooth and on a rough
plane. The first of these systems is Hamiltonian, the second is nonholonomic. We show that, from the viewpoint of monodromy, there is no
difference between the two systems, and thus disprove the conjecture by
Cushman and Duistermaat stating that the topological monodromy gives
a topological obstruction for Hamiltonization of the rolling ellipsoid of
revolution on a rough plane
Topological monodromy as an obstruction to Hamiltonization of nonholonomic systems: pro or contra?
The phenomenon of a topological monodromy in integrable Hamiltonian and nonholonomic systems is discussed. An efficient method for
computing and visualizing the monodromy is developed. The comparative
analysis of the topological monodromy is given for the rolling ellipsoid of
revolution problem in two cases, namely, on a smooth and on a rough
plane. The first of these systems is Hamiltonian, the second is nonholonomic. We show that, from the viewpoint of monodromy, there is no
difference between the two systems, and thus disprove the conjecture by
Cushman and Duistermaat stating that the topological monodromy gives
a topological obstruction for Hamiltonization of the rolling ellipsoid of
revolution on a rough plane
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