We prove that the family of measured dynamical systems which can be realised as uniquely ergodic minimal homeomorphisms on a given manifold (of dimension at least two) is stable under measured extension. As a corollary, any ergodic system with an irrational eigenvalue is isomorphic to a uniquely ergodic minimal homeomorphism on the two-torus. The proof uses the following improvement of Weiss re...

This article is concerned with conjugacy problems arising in homeomorphisms group, Hom(F ), of non-compact subsets F of normed vector spaces E. Given two homeomorphisms f and g in Hom(F ), it is shown how the existence of a conjugacy may be related to the existence of a common generalized eigenfunction of the associated Koopman operators. This common eigenfunction serves to build a topology on ...

We develop a nonlinear Fredholm alternative theory involving k-ball and k-set perturbations of general homeomorphisms as well as of homeomorphisms that are nonlinear Fredholm maps of index zero. Various generalized first Fredholm theorems are given and finite solvability of general (odd) Fredholm maps of index zero is also studied. We apply these results to the unique and finite solvability of ...

Let PL0(I) represent the group of orientation-preserving piecewise-linear homeomorphisms of the unit interval which admit finitely many breaks in slope, under the operation of composition. We find a non-solvable groupW and show thatW embeds in every non-solvable subgroup of PL0(I). We find mild conditions under which other non-solvable subgroups (B, (≀Z≀), (Z≀), and (≀Z)) embed in subgroups of ...

In this article, under suitable assumptions, it is proved that infu∈UΛ E[u] is dual to sup(a,b){ ∫ Ω a(F(x))dx + ∫ Λ b(y)dy}, where, E[u] := ∫ Ω(h(detDu) − F · u)dx. Here, the infimum is performed over UΛ, the set of all orientation-preserving deformations u ∈ C1(Ω)d that are homeomorphisms from Ω̄ onto Λ̄, and the supremum is performed over the set of all upper semicontinuous functions a, b such...

For every finitely generated free group $F$, we construct an irreducible open $3$-manifold $M_F$ whose end set is homeomorphic to a Cantor set, and with the homogeneity of isomorphic $F$. The all self-homeomorphisms that extend homeomorphisms entire $3$-manifold. This extends earlier result constructs, for each abelian $G$, $M_G$ $G$. method used in proof our main also shows if $G$ Cayley graph...

The use of sub-Riemannian geometry on the Heisenberg group H(n) provides a compact picture of symplectic geometry. Any Hamiltonian diffeomorphism on R lifts to a volume preserving bi-Lipschitz homeomorphisms of H(n), with the use of its generating function. Any curve of a flow of such homeomorphisms deviates from horizontality by the Hamiltonian of the flow. From the metric point of view this m...