• Corpus ID: 29775133

BRIEF SURVEY ON THE TOPOLOGICAL ENTROPY 3 Some basic properties of the topological entropy are given in the next two lemmas

@inproceedings{Llibre2015BRIEFSO,
  title={BRIEF SURVEY ON THE TOPOLOGICAL ENTROPY 3 Some basic properties of the topological entropy are given in the next two lemmas},
  author={Jaume Llibre},
  year={2015}
}
In this paper we give a brief view on the topological entropy. The results here presented are well known to the people working in the area, so this survey is mainly for non–experts in the field. 

References

SHOWING 1-10 OF 62 REFERENCES
Lower bounds of the topological entropy for continuous maps of the circle of degree one
The authors give the best lower bound of the topological entropy of a continuous map of the circle of degree one, as a function of the rotation interval. Also, they obtain as a corollary the theorem
Entropy and volume
Abstract An inequality is given relating the topological entropy of a smooth map to growth rates of the volumes of iterates of smooth submanifolds. Applications to the entropy of algebraic maps are
Volume growth and entropy
An inequality is proved, bounding the growth rates of the volumes of iterates of smooth submanifolds in terms of the topological entropy. ForCx-smooth mappings this inequality implies the entropy
Estimates of the topological entropy from below for continuous self-maps on some compact manifolds
Extending our results of [17], we confirm that Entropy Conjecture holds for every continuous self-map of a compact $K(\pi,1)$ manifold with the fundamental group $\pi$ torsion free and virtually
Results and open questions on some invariants measuring the dynamical complexity of a map
Let f be a continuous map on a compact connected Riemannian manifold M . There are several ways to measure the dynamical complexity of f and we discuss some of them. This survey contains some results
Entropy in Smooth Dynamical Systems
The topological entropy of a continuous dynamical system is now well established as an important invariant of the system. It was first defined by Adler, Konheim, and McAndrew [AKM] in 1965 using open
Twist sets for maps of the circle
Abstract Let f be a continuous map of degree one of the circle onto itself. We prove that for every number a from the rotation interval of f there exists an invariant closed set A consisting of
PERIODIC POINTS OF ${\mathcal C}^1$ MAPS AND THE ASYMPTOTIC LEFSCHETZ NUMBER
We study the set of periodic points and the set of periods of different classes of self maps of a compact manifold. We give sufficient conditions in order that these sets be infinite. Our main tools
Entropy conjecture for continuous maps of nilmanifolds
In 1974 Michael Shub asked the following question [29]: When is the topological entropy of a continuous mapping of a compact manifold into itself is estimated from below by the logarithm of the
...
...