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Chaotic dynamics and nonlinear feedback control

J. Baillieul (1985)

Banach Center Publications

Characterizing mildly mixing actions by orbit equivalence of products.

Hawkins, Jane, Silva Cesar, E. (1998)

The New York Journal of Mathematics [electronic only]

Closed orbits in homology classes

Atsushi Katsuda, Toshikazu Sunada (1990)

Publications Mathématiques de l'IHÉS

Conformal measures for rational functions revisited

Manfred Denker, R. Mauldin, Z. Nitecki, Mariusz Urbański (1998)

Fundamenta Mathematicae

We show that the set of conical points of a rational function of the Riemann sphere supports at most one conformal measure. We then study the problem of existence of such measures and their ergodic properties by constructing Markov partitions on increasing subsets of sets of conical points and by applying ideas of the thermodynamic formalism.

Constructing equivariant maps for representations

Stefano Francaviglia (2009)

Annales de l’institut Fourier

We show that if $Γ$ is a discrete subgroup of the group of the isometries of $ℍ^{k}$ , and if $ρ$ is a representation of $Γ$ into the group of the isometries of $ℍ^{n}$ , then any $ρ$ -equivariant map $F : ℍ^{k} \to ℍ^{n}$ extends to the boundary in a weak sense in the setting of Borel measures. As a consequence of this fact, we obtain an extension of a result of Besson, Courtois and Gallot about the existence of volume non-increasing, equivariant maps. Then, we show that the weak extension we obtain is actually a measurable $ρ$ -equivariant...

Construction of 0-1 matrices associated to period-doubling processes.

J. P. Lampreia, A. Rica da Silva, J. Sousa Ramos (1985)

Stochastica

We elaborate a method allowing the determination of 0-1 matrices corresponding to dynamics of the interval having stable, 2k-periodic orbits, k belonging to N. By recurrence on the finite dimensional matrices, we establish the form of the infinite matrices (k --> ∞).

Continuous subadditive processes and formulae for Lyapunov characteristic exponents

Wojciech Słomczyński (1995)

Annales Polonici Mathematici

Asymptotic properties of various semidynamical systems can be examined by means of continuous subadditive processes. To investigate such processes we consider different types of exponents: characteristic, central, singular and global exponents and we study their properties. We derive formulae for central and singular exponents and show that they provide upper bounds for characteristic exponents. The concept of conjugate processes introduced in this paper allows us to find lower bounds for characteristic...

Convex billiards and a theorem by E. Hops.

Misha Bialy (1993)

Mathematische Zeitschrift

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