Toward a Theory of Rank One Attractors
نویسندگان
چکیده
Introduction 1 Statement of results PART I PREPARATION 2 Relevant results from one dimension 3 Tools for analyzing rank one maps PART II PHASE-SPACE DYNAMICS 4 Critical structure and orbits 5 Properties of orbits controlled by critical set 6 Identification of hyperbolic behavior: formal inductive procedure 7 Global geometry via monotone branches 8 Completion of induction 9 Construction of SRB measures PART III PARAMETER ISSUES 10 Dependence of dynamical structures on parameter 11 Dynamics of curves of critical points 12 Derivative growth via statistics 13 Positive measure sets of good parameters APPENDICES
منابع مشابه
Periodically Forced Double Homoclinic Loops to a Dissipative Saddle
In this paper we present a comprehensive theory on the dynamics of strange attractors in periodically perturbed second order differential equations assuming that the unperturbed equations have two homoclinic loops to a dissipative saddle fixed point. We prove the existence of many complicated dynamical objects for given equations, ranging from attractive quasi-periodic torus, to Newhouse sinks ...
متن کاملDynamical profile of a class of rank-one attractors
This paper contains results on the geometric and ergodic properties of a class of strange attractors introduced by Wang and Young [Towards a theory of rank one attractors. Ann. of Math. (2) 167 (2008), 349–480]. These attractors can live in phase spaces of any dimension, and have been shown to arise naturally in differential equations that model several commonly occurring phenomena. Dynamically...
متن کاملFreud, Rank and, the problem of anxiety
Anxiety has always been a phenomenon of great importance among psychoanalysts. Freud, as the founder of psychoanalysis, took much notice of this phenomenon from the beginning of his career, and he was always trying to give a comprehensive explanation for this problem. Therefore, throughout his career, he modified his theories about anxiety frequently, and even one time, he changed his whole the...
متن کاملStrange Attractors in Periodically-kicked Degenerate Hopf Bifurcations
We prove that spiral sinks (stable foci of vector fields) can be transformed into strange attractors exhibiting sustained, observable chaos if subjected to periodic pulsatile forcing. We show that this phenomenon occurs in the context of periodically-kicked degenerate supercritical Hopf bifurcations. The results and their proofs make use of a new k-parameter version of the theory of rank one ma...
متن کاملOn the Moduli Space of non-BPS Attractors for N = 2 Symmetric Manifolds
We study the “flat” directions of non-BPS extremal black hole attractors for N = 2, d = 4 supergravities whose vector multiplets’ scalar manifold is endowed with homogeneous symmetric special Kähler geometry. The non-BPS attractors with non-vanishing central charge have a moduli space described by real special geometry (and thus related to the d = 5 parent theory), whereas the moduli spaces of ...
متن کامل