Isometric immersions and the generalized Laplace and elliptic sinh-Gordon equations.
Isometric immersions of domains of Lobachevski space in Euclidean spaces
Isometric immersions of space forms and soliton theory.
Isomorphic random Bernoulli shifts
We develop a relative isomorphism theory for random Bernoulli shifts by showing that any random Bernoulli shifts are relatively isomorphic if and only if they have the same fibre entropy. This allows the identification of random Bernoulli shifts with standard Bernoulli shifts.
Isomorphism and Hamilton representation of some nonholonomic systems.
Isomorphism of regular Morse dynamical systems
Isomorphism of regular Morse dynamical systems induced by arbitrary blocks
Isomorphisms of Poisson and Jacobi brackets
We present a general theorem describing the isomorphisms of the local Lie algebra structures on the spaces of smooth (real-analytic or holomorphic) functions on smooth (resp. real-analytic, Stein) manifolds, as, for example, those given by Poisson or contact structures. We admit degenerate structures as well, which seems to be new in the literature.
Isospectrality for quantum toric integrable systems
We give a full description of the semiclassical spectral theory of quantum toric integrable systems using microlocal analysis for Toeplitz operators. This allows us to settle affirmatively the isospectral problem for quantum toric integrable systems: the semiclassical joint spectrum of the system, given by a sequence of commuting Toeplitz operators on a sequence of Hilbert spaces, determines the classical integrable system given by the symplectic manifold and commuting Hamiltonians. This type of...
Isotopy of sympletic balls, Gromov' s radius and the structure of ruled symplectic 4-manifolds.
Isotropic characteristic classes
Iterated function systems with continuous place dependent probabilities.
Iteration of a quaternionic quadratic family.
Iterations of rational functions: which hyperbolic components contain polynomials?
Let be the set of all rational maps of degree d ≥ 2 on the Riemann sphere, expanding on their Julia set. We prove that if and all, or all but one, critical points (or values) are in the basin of immediate attraction to an attracting fixed point then there exists a polynomial in the component H(f) of containing f. If all critical points are in the basin of immediate attraction to an attracting fixed point or a parabolic fixed point then f restricted to the Julia set is conjugate to the shift...
Iterations of the Frobenius-Perron operator for parabolic random maps
We describe totally dissipative parabolic extensions of the one-sided Bernoulli shift. For the fractional linear case we obtain conservative and totally dissipative families of extensions. Here, the property of conservativity seems to be extremely unstable.
Iterations over quaternions.
Ito equation as a geodesic flow on
The Ito equation is shown to be a geodesic flow of metric on the semidirect product space , where is the group of orientation preserving Sobolev diffeomorphisms of the circle. We also study a geodesic flow of a metric.
Jet geometrical extension of the KCC-invariants.
∞-jets of diffeomorphisms preserving orbits of vector fields
Let F be a C ∞ vector field defined near the origin O ∈ ℝn, F(O) = 0, and (Ft) be its local flow. Denote by the set of germs of orbit preserving diffeomorphisms h: ℝn → ℝn at O, and let , (r ≥ 0), be the identity component of with respect to the weak Whitney Wr topology. Then contains a subset consisting of maps of the form Fα(x)(x), where α: ℝn → ℝ runs over the space of all smooth germs at O. It was proved earlier by the author that if F is a linear vector field, then = . In this paper we present...
Jordan obstruction to the integrability of Hamiltonian systems with homogeneous potentials
In this paper, we consider the natural complex Hamiltonian systems with homogeneous potential , , of degree . The known results of Morales and Ramis give necessary conditions for the complete integrability of such systems. These conditions are expressed in terms of the eigenvalues of the Hessian matrix calculated at a non-zero point , such that . The main aim of this paper is to show that there are other obstructions for the integrability which appear if the matrix is not diagonalizable....