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Computing explicitly topological sequence entropy: the unimodal case

Victor Jiménez López, Jose Salvador Cánovas Peña (2002)

Annales de l’institut Fourier

Let W ( I ) denote the family of continuous maps f from an interval I = [ a , b ] into itself such that (1) f ( a ) = f ( b ) ∈ { a , b } ; (2) they consist of two monotone pieces; and (3) they have periodic points of periods exactly all powers of 2 . The main aim of this paper is to compute explicitly the topological sequence entropy h D ( f ) of any map f ∈ W ( I ) respect to the sequence D = ( 2 m - 1 ) m = 1 ∞ .

Computing the differential of an unfolded contact diffeomorphism

Klaus Böhmer, Drahoslava Janovská, Vladimír Janovský (2003)

Applications of Mathematics

Consider a bifurcation problem, namely, its bifurcation equation. There is a diffeomorphism Φ linking the actual solution set with an unfolded normal form of the bifurcation equation. The differential D Φ ( 0 ) of this diffeomorphism is a valuable information for a numerical analysis of the imperfect bifurcation. The aim of this paper is to construct algorithms for a computation of D Φ ( 0 ) . Singularity classes containing bifurcation points with c o d i m ≤ 3 , c o r a n k = 1 are considered.

Conditions for integrability of a 3-form

Jiří Vanžura (2017)

Archivum Mathematicum

We find necessary and sufficient conditions for the integrability of one type of multisymplectic 3-forms on a 6-dimensional manifold.

Cone invariance and squeezing properties for inertial manifolds for nonautonomous evolution equations

Norbert Koksch, Stefan Siegmund (2003)

Banach Center Publications

In this paper we summarize an abstract approach to inertial manifolds for nonautonomous dynamical systems. Our result on the existence of inertial manifolds requires only two geometrical assumptions, called cone invariance and squeezing property, and some additional technical assumptions like boundedness or smoothing properties. We apply this result to processes (two-parameter semiflows) generated by nonautonomous semilinear parabolic evolution equations.

Conformal measures and matings between Kleinian groups and quadratic polynomials

Marianne Freiberger (2007)

Fundamenta Mathematicae

Following results of McMullen concerning rational maps, we show that the limit set of matings between a certain class of representations of C₂ ∗ C₃ and quadratic polynomials carries δ-conformal measures, and that if the correspondence is geometrically finite then the real number δ is equal to the Hausdorff dimension of the limit set. Moreover, when f is the limit of a pinching deformation f t 0 ≤ t < 1 we give sufficient conditions for the dynamical convergence of f t .

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.

Conjugacies between ergodic transformations and their inverses

Geoffrey Goodson (2000)

Colloquium Mathematicae

We study certain symmetries that arise when automorphisms S and T defined on a Lebesgue probability space (X, ℱ, μ) satisfy the equation S T = T - 1 S . In an earlier paper [6] it was shown that this puts certain constraints on the spectrum of T. Here we show that it also forces constraints on the spectrum of S 2 . In particular, S 2 has to have a multiplicity function which only takes even values on the orthogonal complement of the subspace f ∈ L 2 ( X , ℱ , μ ) : f ( T 2 x ) = f ( x ) . For S and T ergodic satisfying this equation further constraints arise,...

Conjugacy of normally tangent diffeomorphisms : a tool for treating moduli of stability

Patrick Bonckaert (1990)

Annales de l'institut Fourier

We give sufficient conditions for the conjugacy of two diffeomorphisms coinciding on a common invariant submanifold V and with equal normal derivative; moreover we obtain that the homeomorphism h realizing this conjugacy satisfies additional inequalities. These inequalities, implying also the existence of the normal derivative of h along V, serve to extend this conjugacy towards regions where moduli of stability are present.

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