Let Λ be an isolated non-trivial transitive set of a C1 generic diffeomorphism f ∈ Diff（M）. We show that the space of invariant measures supported on A coincides with the space of accumulation measures of time ave...Let Λ be an isolated non-trivial transitive set of a C1 generic diffeomorphism f ∈ Diff（M）. We show that the space of invariant measures supported on A coincides with the space of accumulation measures of time averages on one orbit. Moreover, the set of points having this property is residual in Λ （which implies that the set of irregular＋ points is also residual in Λ）. As an application, we show that the non-uniform hyperbolicity of irregular＋ points in A with totally 0 measure （resp., the non-uniform hyperbolicity of a generic subset in Λ） determines the uniform hyperbolicity of Λ.展开更多
In this paper we answer all the questions about the conjectures of Glimm and Lax on genericproperties of solutions. We prove that the discotinuous points of almost every solution with L∞,bounded varistion or contrinu...In this paper we answer all the questions about the conjectures of Glimm and Lax on genericproperties of solutions. We prove that the discotinuous points of almost every solution with L∞,bounded varistion or contrinuous data are dense in the upper half-plane minus the closure of the setof central simple waves. It is also proved that if the equation is analytic,then the solutions withpiecewise analytic data are piecewise analytic,and the shock curves are also piecewise analytic. Wedisprove the conjecture which claims that almost every solution with C^k data is 'bad' enough, and provethat every solution with C^k data possesses nice propetied, i.e. when k≥4 the generic property ofsolutions is piecewise C^k,and hence is 'good' enough.For the proof of the generic property withC^k (k≥4) data, the idea of transversality in the theory of singular points is essential.展开更多
We define the notion of evolutes of curves in a hyperbolic plane and establish the relation-ships between singularities of these subjects and geometric invariants of curves under the action of theLorentz group.We also...We define the notion of evolutes of curves in a hyperbolic plane and establish the relation-ships between singularities of these subjects and geometric invariants of curves under the action of theLorentz group.We also describe how we can draw the picture of an evolute of a hyperbolic plane curvein the Poincaré disk.展开更多
基金supported by National Natural Science Foundation(Grant Nos.10671006,10831003)supported by CAPES(Brazil)
文摘Let Λ be an isolated non-trivial transitive set of a C1 generic diffeomorphism f ∈ Diff（M）. We show that the space of invariant measures supported on A coincides with the space of accumulation measures of time averages on one orbit. Moreover, the set of points having this property is residual in Λ （which implies that the set of irregular＋ points is also residual in Λ）. As an application, we show that the non-uniform hyperbolicity of irregular＋ points in A with totally 0 measure （resp., the non-uniform hyperbolicity of a generic subset in Λ） determines the uniform hyperbolicity of Λ.
文摘In this paper we answer all the questions about the conjectures of Glimm and Lax on genericproperties of solutions. We prove that the discotinuous points of almost every solution with L∞,bounded varistion or contrinuous data are dense in the upper half-plane minus the closure of the setof central simple waves. It is also proved that if the equation is analytic,then the solutions withpiecewise analytic data are piecewise analytic,and the shock curves are also piecewise analytic. Wedisprove the conjecture which claims that almost every solution with C^k data is 'bad' enough, and provethat every solution with C^k data possesses nice propetied, i.e. when k≥4 the generic property ofsolutions is piecewise C^k,and hence is 'good' enough.For the proof of the generic property withC^k (k≥4) data, the idea of transversality in the theory of singular points is essential.
文摘We define the notion of evolutes of curves in a hyperbolic plane and establish the relation-ships between singularities of these subjects and geometric invariants of curves under the action of theLorentz group.We also describe how we can draw the picture of an evolute of a hyperbolic plane curvein the Poincaré disk.
