In the current paper we study in more detail some properties of the absolutely continuous invariant measures constructed in the course of the proof of Jakobson's Theorem. In particular, we show that the density of the invariant measure is continuous at Misiurewicz points. From this we deduce that the Lyapunov exponent is also continuous at these points (our considerations apply just to the para...

We consider normal covers of CP with abelian deck group, branched over at most four points. Families of such covers yield arithmetic Teichmüller curves, whose period mapping may be described geometrically in terms of Schwarz triangle mappings. These Teichmüller curves are generated by abelian square-tiled surfaces. We compute all individual Lyapunov exponents for abelian squaretiled surfaces, a...

This note presents a new approach to deriving stability conditions for continuous-time linear systems interconnected with a saturation. The method presented here can be extended to handle a deadzone, or in general, nonlinearities in the form of piecewise linear functions. By representing the saturation as a constrained optimization problem, the necessary (Kuhn–Tucker) conditions for optimality ...

This paper illustrates the application of recent research in region-of-attraction analysis for nonlinear hybrid limit cycles. Three example systems are analyzed in detail: the van der Pol oscillator, the “rimless wheel”, and the “compass gait”, the latter two being simplified models of underactuated walking robots. The method used involves decomposition of the dynamics about the target cycle in...

Lyapunov exponents, important invariants of a complicated dynamical process, can be difficult to determine from experimental data. In particular, when using embedding theory to build chaotic attractors in a reconstruction space, extra “spurious” Lyapunov exponents can arise that are not Lyapunov exponents of the original system. By studying the local linearization matrices that are key to a pop...

In this paper we propose an unified construction of Lyapunov functions based on Lur’e type functions that allows us to go from Persidskii’s to pure quadratic functions. Such Lyapunov functions allows the establishment of the absolute stability of nonlinear systems with nonlinearities belonging to given sectors. The sectors can be finite or infinite. An stability criterion is formulated in terms...

The equivalence between robustness to perturbations and the existence of a continuous Lyapunov-like mapping is established in a setting of multivalued discrete-time dynamics for a property sometimes called semistability. This property involves a set consisting of Lyapunov stable equilibria and surrounded by points from which every solution converges to one of these equilibria. As a consequence ...

In this paper we show some symmetry properties of Lyapunov exponents of a dynamical system when the linearized problem evolves on a quadratic group, X HX = H , with H orthogonal. It is well understood that in this case the exponents are symmetric with respect to the origin. Here, we give lower bounds on the number of Lyapunov exponents which are 0, and show that some Lyapunov exponents may have...

The fractal dimension of an attracting torus Tk in lR x T" is shown to be almost always equal to the Lyapunov dimension as predicted by a previous conjecture. The cases studied here can have several Lyapunov nulJ!bers greater than I and several less than I

We study convex optimization problems with side constraints in a multiclass M/G/1 queue with controllable service rates. In the simplest problem of optimizing linear costs with fixed service rate, the cμ rule is known to be optimal. A natural question to ask is whether such simple policies exist for more complex control objectives. In this paper, combining the achievable region approach in queu...