On the Lengths of Closed Geodesics on Almost Round Spheres.
On the minimum dilatation of pseudo-Anosov homeromorphisms on surfaces of small genus
We find the minimum dilatation of pseudo-Anosov homeomorphisms that stabilize an orientable foliation on surfaces of genus three, four, or five, and provide a lower bound for genus six to eight. Our technique also simplifies Cho and Ham’s proof of the least dilatation of pseudo-Anosov homeomorphisms on a genus two surface. For genus to , the minimum dilatation is the smallest Salem number for polynomials of degree .
On the Morse Complex.
On the rate of mixing of Axiom A flows.
On the relationship between hyperbolic and cone-hyperbolic structures in metric spaces
We give necessary and sufficient conditions for topological hyperbolicity of a homeomorphism of a metric space, restricted to a given compact invariant set. These conditions are related to the existence of an appropriate finite covering of this set and a corresponding cone-hyperbolic graph-directed iterated function system.
On the spectral theory and dynamics of asymptotically hyperbolic manifolds
We present a brief survey of the spectral theory and dynamics of infinite volume asymptotically hyperbolic manifolds. Beginning with their geometry and examples, we proceed to their spectral and scattering theories, dynamics, and the physical description of their quantum and classical mechanics. We conclude with a discussion of recent results, ideas, and conjectures.
On the structure of the space of continuous maps with zero topological entropy
On the Time Evolution of Statistical States for Anosov Systems.
On the topological equivalence between Anosov flows on the three-manifolds.
On the unstable directions and Lyapunov exponents of Anosov endomorphisms
Unlike in the invertible setting, Anosov endomorphisms may have infinitely many unstable directions. Here we prove, under the transitivity assumption, that an Anosov endomorphism of a closed manifold M is either special (that is, every x ∈ M has only one unstable direction), or for a typical point in M there are infinitely many unstable directions. Another result is the semi-rigidity of the unstable Lyapunov exponent of a codimension one Anosov endomorphism that is C¹-close to a linear endomorphism...
On three-periodic trajectories of multi-dimensional dual billiards.
On Ω-stability and structural stability of endomorphisms satisfying Axiom A
One-dimensional and two-dimensional dynamics of cubic maps.
One-Parameter Flows with the Pseudo Orbit Tracing Property.
Optimal, adaptive and single state feedback control for a 3D chaotic system with golden proportion equilibria
In this paper, the problems on purposefully controlling chaos for a three-dimensional quadratic continuous autonomous chaotic system, namely the chaotic Pehlivan-Uyaroglu system are investigated. The chaotic system, has three equilibrium points and more interestingly the equilibrium points have golden proportion values, which can generate single folded attractor. We developed an optimal control design, in order to stabilize the unstable equilibrium points of this system. Furthermore, we propose...
Optimality of Ruelle's bound for the domain of meromorphy of generalized zeta functions
Orbit counting for some discrete groups acting on simply connected manifolds with negative curvature.
Orientation Reversing Morse-Smale Diffeomorphisms of S2.
Outer boundaries of self-similar tiles.
Packing dimensions, transversal mappings and geodesic flows.