Involutive distributions, invariant manifolds, and defining equations.
IP-Dirichlet measures and IP-rigid dynamical systems: an approach via generalized Riesz products
If is a strictly increasing sequence of integers, a continuous probability measure σ on the unit circle is said to be IP-Dirichlet with respect to if as F runs over all non-empty finite subsets F of ℕ and the minimum of F tends to infinity. IP-Dirichlet measures and their connections with IP-rigid dynamical systems have recently been investigated by Aaronson, Hosseini and Lemańczyk. We simplify and generalize some of their results, using an approach involving generalized Riesz products.
Irrational life.
Irreducible complexity of iterated symmetric bimodal maps.
Irregular attractors.
Isometric extensions, 2-cocycles and ergodicity of skew products
We establish existence and uniqueness of a canonical form for isometric extensions of an ergodic non-singular transformation T. This is applied to describe the structure of commutors of the isometric extensions. Moreover, for a compact group G, we construct a G-valued T-cocycle α which generates the ergodic skew product extension and admits a prescribed subgroup in the centralizer of .
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...