![]() Triangles and rectangles in Jordan loops. I'll describe some computer experiments I'veĭone, and also some results I have, about inscribing Inscribing Triangles and Rectangles in Jordan Curves We will also describe transitive sets in the non-conservative case, showing that such a set must belong to one of the following possibilities:ģ- The dynamics over this set is infinitely renormalizable, and semi-conjugate to that of an odometer map. We will show that if such a system is conservative, then the dynamics is in many ways similar to that of a fully integrable system, extending a result of Franks and Handel previously known for diffeomorphisms. We will describe what this new criterion is, and apply it to obtain a description of the possible behaviors of dynamical systems on surfaces with null genus with zero topological entropy. This is done using the machinery of Brouwer-Le Calvez foliations and a related dynamical forcing theory. In this work we derive a new criterion to detect the existence of positive entropy (and of topological horseshoes) for surface homeomorphisms in the isotopy class of the identity. Homeomorphisms of Surfaces with Zero Entropy Theory is used to understand integral quadratic forms.įeb 22: Fabio Tal (Universidade de São Paulo) Recent resolution of this problem based on a joint work with $n \geq 3$, there exists a polynomial search bound for $X$ in Was known for indefinite forms until the work of C. For definite forms one can construct a simpleĭecision procedure. Unimodular integral matrix $X$ satisfying $A=X^tBX$, where $X^t$ is the Symmetric $n$-by-$n$ integral matrices $A$ and $B$, whether there is a Whether two given integral quadratic forms are equivalent.įormulated in terms of matrices the problem asks, for given Masser’s Conjecture on Equivalence of Integral Quadratic FormsĪ classical problem in the theory of quadratic forms is to decide I’ll give some indication of the general approach there. ![]() Proved to be stable (entropy, pressure, equilibrium states), and This work forms part of a paper with Neilĭobbs, where more general thermodynamic properties are I’ll give minimal conditions for aĬlass of non-uniformly hyperbolic interval maps to satisfy this Weak form of stability if these measures change continuously Possessing a canonical measure (an invariant measureĪbsolutely continuous w.r.t. ![]() Given a family of interval maps, each map Stability of Measures in Interval Dynamics The results in this talk are joint work with Yun Yang.įeb 8: Mike Todd (University of St. We also discuss the regularity of the localizedĮntropy function on the boundary of the generalized rotation Measures and the boundary of higher dimensional generalized Relationship between the distribution of the zero-temperature Locally constant functions over subshifts of finite type via their In this talk we discuss a topological classification of ![]() Complex Analysis and Dynamics Seminar at CUNY's GCįeb 1: Christian Wolf (City College and Graduate Center of CUNY)Ī Topological Classification of Locally Constant Potentials Providence: American Mathematical Society. Ordinary Differential Equations and Dynamical Systems. An introduction to symbolic dynamics and coding. ISBN 0-19-853390-X (Provides a short expository introduction, with exercises, and extensive references.) Keane, Ergodic theory and subshifts of finite type, (1991), appearing as Chapter 2 in Ergodic Theory, Symbolic Dynamics and Hyperbolic Spaces, Tim Bedford, Michael Keane and Caroline Series, Eds.
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