Let f : X â†’ X be the restriction to a hyperbolic basic set of a smooth diffeomorphism. We find several criteria for transitivity of noncompact connected Lie group extensions. As a consequence, weâ€¦ (More)

In this paper we obtain results about the regularity of the transfer map between two cocycles over an Anosov system, with values in either a diffeomorphism or a Lie group. We also explain how certainâ€¦ (More)

Let f : X â†’ X be the restriction to a hyperbolic basic set of a smooth diffeomorphism. We show that in the class of C, r > 0, cocycles with fiber special Euclidean group SE(n) those that areâ€¦ (More)

Consider the set B = [0, 1] endowed with the operations âŠ• = max,âˆ§ = min. This is a well-known distributive lattice, and like any distributive lattice it can be considered as a semiring equipped withâ€¦ (More)

We prove certain rigidity properties of higher-rank abelian product actions of the typeÎ± Ã— IdN : Z â†’ Diff (M Ã— N), whereÎ± is (TNS) (i.e. is hyperbolic and has some special structure of its stableâ€¦ (More)

We investigate tiling problems for regions in a square lattice by ribbon L-shaped tetrominoes. Our results show that tiling of the first quadrant by ribbon L-tetrominoes is possible only if itâ€¦ (More)

Let f : X â†’ X be the restriction to a hyperbolic basic set of a smooth diffeomorphism. If G is the special Euclidean group SE(2) we show that in the set of C2 G-extensions of f there exists an openâ€¦ (More)

We consider cocycles over certain hyperbolic R actions, k â‰¥ 2, and show rigidity properties for cocycles with values in a Lie group or a diffeomorphism group, which are close to identity on a set ofâ€¦ (More)

Let Tn be the set of ribbon L-shaped n-ominoes for some n â‰¥ 4 even, and let T + n be Tn with an extra 2 Ã— 2 square. We investigate signed tilings of rectangles by Tn and T + n . We show that aâ€¦ (More)

We show that the least number of cells (the gap number) one needs to take out from a rectangle with integer sides of length at least 2 in order to be tiled by ribbon right trominoes is less than orâ€¦ (More)