Search results for "Mathematics::Dynamical Systems"
showing 10 items of 113 documents
A note on higher order Melnikov functions
2005
We present several classes of planar polynomial Hamilton systems and their polynomial perturbations leading to vanishing of the first Melnikov integral. We discuss the form of higher order Melnikov integrals. In particular, we present new examples where the second order Melnikov integral is not an Abelian integral.
On hyperbolic type involutions
2001
We give a bound on the number of hyperbolic knots which are double covered by a fixed (non hyperbolic) manifold in terms of the number of tori and of the invariants of the Seifert fibred pieces of its Jaco-Shalen-Johannson decomposition. We also investigate the problem of finding the non hyperbolic knots with the same double cover of a hyperbolic one and give several examples to illustrate the results.
IFS attractors and Cantor sets
2006
Abstract We build a metric space which is homeomorphic to a Cantor set but cannot be realized as the attractor of an iterated function system. We give also an example of a Cantor set K in R 3 such that every homeomorphism f of R 3 which preserves K coincides with the identity on K.
Approximating hidden chaotic attractors via parameter switching.
2018
In this paper, the problem of approximating hidden chaotic attractors of a general class of nonlinear systems is investigated. The parameter switching (PS) algorithm is utilized, which switches the control parameter within a given set of values with the initial value problem numerically solved. The PS-generated attractor approximates the attractor obtained by averaging the control parameter with the switched values, which represents the hidden chaotic attractor. The hidden chaotic attractors of a generalized Lorenz system and the Rabinovich-Fabrikant system are simulated for illustration. In Refs. 1–3, it is proved that the attractors of a chaotic system, considered as the unique numerical …
The arithmetic decomposition of central Cantor sets
2018
Abstract Every central Cantor set of positive Lebesgue measure is the arithmetic sum of two central Cantor sets of Lebesgue measure zero. Under some mild condition this result can be strengthened by stating that the summands can be chosen to be C s regular if the initial set is of this class.
Rigidity of quasisymmetric mappings on self-affine carpets
2016
We show that the class of quasisymmetric maps between horizontal self-affine carpets is rigid. Such maps can only exist when the dimensions of the carpets coincide, and in this case, the quasisymmetric maps are quasi-Lipschitz. We also show that horizontal self-affine carpets are minimal for the conformal Assouad dimension.
Topological lower bounds on the distance between area preserving diffeomorphisms
2000
Area preserving diffeomorphisms of the 2-disk which are Identity near the boundary form a group which can be equipped, using theL2-norm on its Lie algebra, with a right invariant metric. In this paper we give a lower bound on the distance between diffeomorphisms which is invariant under area preserving changes of coordinates and which improves the lower bound induced by the Calabi invariant. In the case of renormalizable and infinitely renormalizable maps, our estimate can be improved and computed.
Symbolic Dynamics of Geodesic Flows on Trees
2019
In this chapter, we give a coding of the discrete-time geodesic ow on the nonwandering sets of quotients of locally finite simplicial trees X without terminal vertices by nonelementary discrete subgroups of Aut(X) by a subshift of finite type on a countable alphabet.
Explicit Measure Computations for Simplicial Trees and Graphs of Groups
2019
In this chapter, we compute skinning measures and Bowen{Margulis measures for some highly symmetric simplicial trees X endowed with a nonelementary discrete subgroup Г of Aut(X).
Three viewpoints on the integral geometry of foliations
1999
We deal with three different problems of the multidimensional integral geometry of foliations. First, we establish asymptotic formulas for integrals of powers of curvature of foliations obtained by intersecting a foliation by affine planes. Then we prove an integral formula for surfaces of contact of an affine hyperplane with a foliation. Finally, we obtain a conformally invariant integral-geometric formula for a foliation in three-dimensional space.