Wyniki wyszukiwania - Biblioteka Nauki

Nowa wersja platformy, zawierająca wyłącznie zasoby pełnotekstowe, jest już dostępna.
Przejdź na https://bibliotekanauki.pl

Ograniczanie wyników

Znaleziono wyników: 5

Liczba wyników na stronie

Wyniki wyszukiwania

Sortuj według:

Ogranicz wyniki do:

For almost every tent map, the turning point is typical

100%

Bruin H.

Fundamenta Mathematicae

1998

tom 155

nr 3

215-235

Let $T_a$ be the tent map with slope a. Let c be its turning point, and $μ_a$ the absolutely continuous invariant probability measure. For an arbitrary, bounded, almost everywhere continuous function g, it is shown that for almost every a, $ʃ g dμ_a = lim_{n → ∞} \frac1n ∑_{i=0}^{n-1} g(T^i_a(c))$. As a corollary, we deduce that the critical point of a quadratic map is generically not typical for its absolutely continuous invariant probability measure, if it exists.

Inverse limit spaces of post-critically finite tent maps

100%

Bruin H.

Fundamenta Mathematicae

2000

tom 165

nr 2

125-138

Let (I,T) be the inverse limit space of a post-critically finite tent map. Conditions are given under which these inverse limit spaces are pairwise nonhomeomorphic. This extends results of Barge & Diamond [2].

Subcontinua of inverse limit spaces of unimodal maps

63%

Brucks K. , Bruin H.

Fundamenta Mathematicae

1999

tom 160

nr 3

219-246

We discuss the inverse limit spaces of unimodal interval maps as topological spaces. Based on the combinatorial properties of the unimodal maps, properties of the subcontinua of the inverse limit spaces are studied. Among other results, we give combinatorial conditions for an inverse limit space to have only arc+ray subcontinua as proper (non-trivial) subcontinua. Also, maps are constructed whose inverse limit spaces have the inverse limit spaces of a prescribed set of periodic unimodal maps as subcontinua.

Existence of quadratic Hubbard trees

51%

Bruin H. , Kaffl A. , Schleicher D.

Fundamenta Mathematicae

2009

tom 202

nr 3

251-279

A (quadratic) Hubbard tree is an invariant tree connecting the critical orbit within the Julia set of a postcritically finite (quadratic) polynomial. It is easy to read off the kneading sequences from a quadratic Hubbard tree; the result in this paper handles the converse direction. Not every sequence on two symbols is realized as the kneading sequence of a real or complex quadratic polynomial. Milnor and Thurston classified all real-admissible sequences, and we give a classification of all complex-admissible sequences in [BS]. In order to do this, we show here that every periodic or preperiodic sequence is realized by a unique abstract Hubbard tree. Real or complex admissibility of the sequence depends on whether this abstract tree can be embedded into the real line or complex plane so that the dynamics preserves the embedded, and this can be studied in terms of branch points of the abstract Hubbard tree.

Minimal nonhomogeneous continua

51%

Bruin H. , Kolyada S. , Snoha L. u.

Colloquium Mathematicum

2003

tom 95

nr 1

123-132

We show that there are (1) nonhomogeneous metric continua that admit minimal noninvertible maps but have the fixed point property for homeomorphisms, and (2) nonhomogeneous metric continua that admit both minimal noninvertible maps and minimal homeomorphisms. The former continua are constructed as quotient spaces of the torus or as subsets of the torus, the latter are constructed as subsets of the torus.