Short Cycles in Repeated Exponentiation Modulo a Prime (2009)
Glebsky, Lev, Shparlinski, Igor E.
Given a prime $p$, we consider the dynamical system generated by repeated exponentiations modulo $p$, that is, by the map $u \mapsto f_g(u)$, where $f_g(u) \equiv g^u \pmod p$ and $0 \le f_g(u) \le...
On low rank perturbation of matrices (2008)
Glebsky, Lev, Rivera, Luis Manuel
The article is devoted to different aspects of the question "What can be done with a matrix by low rank perturbation?" It is proved that one can change a geometrically simple spectrum drastically by...
Almost solutions of equations in permutations (2007)
Glebsky, Lev, Rivera, Luis Manuel
We will say that the permutations f_1,...,f_n is an e-solution of an equation if the normalized Hamming distance between its l.h.p. and r.h.p. is less than e. We give a sufficient conditions when...
Sofic groups and profinite topology on free groups (2007)
Glebsky, Lev, Martinez, Luis Manuel Rivera
We give a definition of weakly sofic groups (w-sofic groups). Our definition is rather natural extension of the definition of sofic groups where instead of Hamming metric on symmetric groups we use...
Measures related to (e,n)-complexity functions (2007)
Afraimovich, Valentin, Glebsky, Lev
The (e,n)-complexity functions describe total instability of trajectories in dynamical systems. They reflect an ability of trajectories going through a Borel set to diverge on the distance $\epsilon$...
Stefan Gerhold, Carsten Schneider, Lev Glebsky, Lomas A, Slp México, Howard Weiss, ...
The Schelling segregation models are “agent based ” population models, where individual members of the population (agents) interact directly with other agents and move in space and time. In this...
The conjecture cr(C_m\times C_n)=(m-2)n is true for all but finitely many n, for each m (2000)
Glebsky, Lev, Salazar, Gelasio
It has been long congectured that the crossing number of $C_m\times C_n$ is $(m-2)n$ for $2