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In this paper we first give an overview of the methods of analysis of time series in terms of correlation integrals, which were developed for time series generated by deterministic systems. From the extremal value theory one obtains asymptotic information on the behaviour of the correlation...
LetH be a germ of holomorphic diffeomorphism at 0 ∈ ℂ. Using the existence theorem for quasi-conformal mappings, it is possible to prove that there exists a multivalued germS at 0, such thatS(ze
)=H○S(z) (1). IfH
λ is an unfolding of diffeomorphisms depending on λ ∈ (ℂ,0), withH
A simple example is considered of Hill's equation
$$\ddot x + (a^2 + bp(t))x = 0$$
, where the forcing termp, instead of periodic, is quasi-periodic with two frequencies. A geometric exploration is carried out of certain resonance tongues, containing instability pockets. This phenomenon in the...
For ordinary abelian varieties in characteristicp>0, we define an analogue of the period lattice and of the parametrization by ℂ
and give some applications.
This paper deals with global injectivity of vector fields defined on euclidean spaces. Our main result establishes a version of Rolle's Theorem under generalized Palais-Smale conditions. As a consequence of this, we prove global injectivity for a class of vector fields defined on n-dimensional...
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...
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