Topological Birkhoff
نویسندگان
چکیده
One of the most fundamental mathematical contributions of Garrett Birkhoff is the HSP theorem, which implies that a finite algebra B satisfies all equations that hold in a finite algebra A of the same signature if and only if B is a homomorphic image of a subalgebra of a finite power of A. On the other hand, if A is infinite, then in general one needs to take an infinite power in order to obtain a representation of B in terms of A, even
منابع مشابه
Topological transitivity
The concept of topological transitivity goes back to G. D. Birkhoff [1]
متن کاملThe Topological Entropy and Invariant Circles of an Area Preserving Twistmap
Indeed, in [3] they showed that, if one of the invariant circles of f is missing, then for some p and q with gcd(p; q) = 1 the map must have a periodic orbit of type (p; q) which is not a Birkhoff orbit. On the other hand, Boyland showed in [2] that a twistmap with a non Birkhoff periodic orbit of type (p; q) (gcd(p; q) = 1 must have positive topological entropy, which clearly implies the theorem.
متن کاملOn Two Recurrence Problems
We review some aspects of recurrence in topological dynamics and focus on two open problems. The first is an old one concerning the relation between Poincaré and Birkhoff recurrence; the second, due to Boshernitzan, is about moving recurrence. We provide a partial answer to a topological version of the moving recurrence problem.
متن کاملMultifractal Analysis of Hyperbolic Flows
We establish the multifractal analysis of hyperbolic flows and of suspension flows over subshifts of finite type. A non-trivial consequence of our results is that for every Hölder continuous function noncohomologous to a constant, the set of points without Birkhoff average has full topological entropy.
متن کاملHigher Order Birkhoff Averages
There are well-known examples of dynamical systems for which the Birkhoff averages with respect to a given observable along some or all of the orbits do not converge. It has been suggested that such orbits could be classified using higher order averages. In the case of a bounded observable, we show that a classical result of G.H. Hardy implies that if the Birkhoff averages do not converge, then...
متن کاملBirkhoff Averages for Hyperbolic Flows: Variational Principles and Applications
Abstract. We establish a higher-dimensional version of multifractal analysis for hyperbolic flows. This means that we consider simultaneously the level sets of several Birkhoff averages. Examples are the Lyapunov exponents as well as the pointwise dimension and the local entropy of a given measure. More precisely, we consider multifractal spectra associated to multi-dimensional parameters, obta...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
- CoRR
دوره abs/1203.1876 شماره
صفحات -
تاریخ انتشار 2012