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Articles 1 - 8 of 8
Full-Text Articles in Physical Sciences and Mathematics
Symmetric Random Walks On Homeo+(R), B. Deroin, V. Klepstyn, A. Navas, Kamlesh Parwani
Symmetric Random Walks On Homeo+(R), B. Deroin, V. Klepstyn, A. Navas, Kamlesh Parwani
Kamlesh Parwani
We study symmetric random walks on finitely generated groups of orientation-preserving homeomorphisms of the real line. We establish an oscillation property for the induced Markov chain on the line that implies a weak form of recurrence. Except for a few special cases, which can be treated separately, we prove a property of "global stability at a finite distance": roughly speaking, there exists a compact interval such that any two trajectories get closer and closer whenever one of them returns to the compact interval. The probabilistic techniques employed here lead to interesting results for the study of group actions on the …
Harmonic Functions On R-Covered Foliations And Group Actions On The Circle, Sergio Fenley, Renato Feres, Kamlesh Parwani
Harmonic Functions On R-Covered Foliations And Group Actions On The Circle, Sergio Fenley, Renato Feres, Kamlesh Parwani
Kamlesh Parwani
Let (M,F) be a compact codimension-one foliated manifold whose leaves are equipped with Riemannian metrics, and consider continuous functions on M that are harmonic along the leaves of F. If every such function is constant on leaves we say that (M,F) has the Liouville property. Our main result is that codimension-one foliated bundles over compact negatively curved manifolds satisfy the Liouville property. Related results for R-covered foliations, as well as for discrete group actions and discrete harmonic functions, are also established.
C^1 Actions Of The Mapping Class Group On The Circle, Kamlesh Parwani
C^1 Actions Of The Mapping Class Group On The Circle, Kamlesh Parwani
Kamlesh Parwani
Let S be a connected orientable surface with finitely many punctures, finitely many boundary components, and genus at least 6. Then any C^1 action of the mapping class group of S on the circle is trivial. The techniques used in the proof of this result permit us to show that products of Kazhdan groups and certain lattices cannot have C^1 faithful actions on the circle. We also prove that for n > 5, any C^1 action of Aut(F_n) or Out(F_n) on the circle factors through an action of Z/2Z.
Fixed Points Of Abelian Actions On S2, John Franks, Michael Handel, Kamlesh Parwani
Fixed Points Of Abelian Actions On S2, John Franks, Michael Handel, Kamlesh Parwani
Kamlesh Parwani
We prove that if $F$ is a finitely generated abelian group of orientation preserving $C^1$ diffeomorphisms of $R^2$ which leaves invariant a compact set then there is a common fixed point for all elements of $F.$ We also show that if $F$ is any abelian subgroup of orientation preserving $C^1$ diffeomorphisms of $S^2$ then there is a common fixed point for all elements of a subgroup of $F$ with index at most two.
Fixed Points Of Abelian Actions, John Franks, Michael Handel, Kamlesh Parwani
Fixed Points Of Abelian Actions, John Franks, Michael Handel, Kamlesh Parwani
Kamlesh Parwani
We prove that if $\F$ is an abelian group of $C^1$ diffeomorphisms isotopic to the identity of a closed surface $S$ of genus at least two then there is a common fixed point for all elements of $\F.$
Simple Braids For Surface Homeomorphisms, Kamlesh Parwani
Simple Braids For Surface Homeomorphisms, Kamlesh Parwani
Kamlesh Parwani
Let S be a compact, oriented surface with negative Euler characteristic and f:S→S be a homeomorphism isotopic to the identity. If there exists a periodic orbit with a non-zero rotation vector (p→,q), then there exists a simple braid with the same rotation vector.
Actions Of Sl(N,Z) On Homology Spheres, Kamlesh Parwani
Actions Of Sl(N,Z) On Homology Spheres, Kamlesh Parwani
Kamlesh Parwani
Any continuous action of SL(n,Z), where n > 2, on a r-dimensional mod 2 homology sphere factors through a finite group action if r < n - 1. In particular, any continuous action of SL(n+2,Z) on the n-dimensional sphere factors through a finite group action.
Monotone Periodic Orbits For Torus Homeomorphisms, Kamlesh Parwani
Monotone Periodic Orbits For Torus Homeomorphisms, Kamlesh Parwani
Kamlesh Parwani
Let f be a homeomorphism of the torus isotopic to the identity and suppose that there exists a periodic orbit with a non-zero rotation vector (p/q,r/q), then f has a topologically monotone periodic orbit with the same rotation vector.