The Furstenberg lemma characterizes amenability

We characterize amenability in terms of the existence of equivariant assignments of measures for cocycles into the homeomorphism group of a single compact metric space.

     

The Dirac bracket

The possibility of giving a geometrical meaning to Hamiltonian dynamics in the presence of second-class constraints by using the Dirac bracket to define a symplectic structure on the phase space is discussed.In memory of Mikhail Konstantinovich PolivanovV. A. Steklov Mathematics Institute, Russian Academy of Sciences; Higher College of Mathematical Physics of the Independent Moscow University. Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 92, No. 3, pp. 451–456, September, 1992.     

广义近似空间的粗糙同胚与拓扑同胚

对广义近似空间之间的映射引入并刻画了粗糙连续性和拓扑连续性,探讨了他们的性质及相互关系.证明了两个粗糙连续映射的复合还是粗糙连续的,每个粗糙连续的映射都是拓扑连续的.在此基础上引入了粗糙同胚性质和拓扑同胚性质的概念,证明了拓扑同胚性质均为粗糙同胚性质并考察了广义近似空间的诸如分离性、连通性、紧性等的粗糙同胚不变性和拓扑同胚不变性.     

Reversible interval homeomorphisms

A characterization of continuously reversible self-mappings of an open interval, that is, compositions of two continuous involutions, is proved.     

The colorings of homeomorphisms on connected graphs

In this paper, we decide the exact value of the color number of a fixed point free homeomorphism on a connected locally finite graph. We prove that for every fixed-point free homeomorphism from a connected locally finite graph into itself, the greatest common divisor of all period for its map is equal to one or three if and only if its color number is 4.     

On quasisymmetric homeomorphisms

We introduce and study some operators and functions induced by a quasisymmetric homeomorphism. By means of these operators and functions, we study when a quasisymmetric homeomorphism is symmetric or even belongs to the Weil-Petersson class.     

The groups of quasiconformal homeomorphisms on Riemann surfaces

Suppose is a connected Riemann surface. Let denote the homeomorphism group of with the compact-open topology, and denote the subgroup of quasiconformal mappings of onto itself, and let and denote the identity components of and respectively. In this paper we show that the pair is an -manifold, and determine their topological types.

     

On quasimonotone increasing homeomorphisms

Let f ? C(\Bbb Rⁿ,\Bbb Rⁿ) f\in C(\Bbb R^n,\Bbb R^n) be quasimonotone increasing such that Y(f(y)-f(x)) ￡ -c Y(y-x) (x << y) \Psi (f(y)-f(x)) \!\le -c \Psi (y-x) (x\ll y) for a linear and strictly positive functional Y \Psi and c > 0. We prove that f is a homeomorphism with decreasing and Lipschitz continuous inverse and we prove the global asymptotic stability of the equilibrium solution of x￠=f(x) x'=f(x) .     

The bracket semigroup of knots

The paper is devoted to a coding of links with marked point on an oriented component by means of regular bibracket structures, i.e., by some words in the alphabet (,),[,]. In this way we naturally obtain the semigroup of knots with concatenation as the semigroup operation, and with the equivalence classes modulo so-called “global relations” as elements. An important step in the construction of this semigroup is the coding of links with the help of so-calledd-diagrams. Translated fromMatematicheskie Zametki, Vol. 67, No. 4, pp. 549–562, April, 2000.     

The fixed subgroups of homeomorphisms of Seifert manifolds

Let M be a compact connected orientable Seifert manifold with hyperbolic orbifold B M,and fπ : π1(M) →π1(M) be an automorphism induced by an orientation-reversing homeomorphism f of M. We give a bound on the rank of the fixed subgroup of fπ, namely, rank Fix(fπ) 2rankπ1(M),which is an analogue of inequalities on surface groups and hyperbolic 3-manifold groups.     

The ACL property of homeomorphisms under weak conditions

Suppose thatD is a domain in andy=f(x)∶D→R ⁿ is a homeomorphism. We prove that if the modulus dilatationK(x, f) satisfies the condition A thenf(x) is ACL. Project supported by the National Natural Science Foundation of China and JTU     

On critical circle homeomorphisms

We prove that an analytic circle homeomorphism without periodic orbits is conjugated to the linear rotation by a quasi-symmetric map if an only if its rotation number is of constant type. Next, we consider automorphisms of quasi-conformal Jordan curves, without periodic orbits and holomorphic in a neighborhood. We prove a Denjoy theorem that such maps are conjugated to a rotation on the circle.Dedicated to the memory of R. MañéPartially supported by NSF grant DMS-9704368 and the Sloan Foundation.