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We present a topological technique for analyzing dynamical systems with complex behavior, based on the general notion of covering relations. Our method can be used to study multidimensional dynamical systems with an arbitrary number of ‘topologically’ expanding directions.

We use topological methods to investigate some recently proposed mechanisms of instability (Arnol’d diffusion) in Hamiltonian systems. In these mechanisms, chains of heteroclinic connections between whiskered tori are constructed, based on the existence of a normally hyperbolic manifold Λ, so that: (a) the manifold Λ is covered rather densely by transitive… (More)

- Marian Gidea
- 2007

We consider a dynamical system that exhibits transition chains of invariant tori alternating with Birkhoff zones of instability in a 2-dimensional center manifold. It is known that there exist orbits that shadow the transition chains. It is also known that there exist orbits that cross the Birkhoff zones of instability. We describe a topological mechanism… (More)

- Edward Belbruno, Marian Gidea, Francesco Topputo
- SIAM J. Applied Dynamical Systems
- 2010

The concept of weak stability boundary has been successfully used in the design of several fuel efficient space missions. In this paper we give a rigorous definition of the weak stability boundary in the context of the planar circular restricted three-body problem, and we provide a geometric argument for the fact that, for some energy range, the points in… (More)

- Marian Gidea, James D. Meiss, Ilie Ugarcovici, Howard Weiss
- Journal of biological dynamics
- 2011

Computer simulations have shown that several classes of population models, including the May host-parasitoid model and the Ginzburg-Taneyhill 'maternal-quality' single species population model, exhibit extremely complicated orbit structures. These structures include islands-around-islands, ad infinitum, with the smaller islands containing stable periodic… (More)

We consider transition tori of Arnold which have topologically crossing heteroclinic connections. We prove the existence of shadowing orbits to a bi-infinite sequence of tori, and of symbolic dynamics near a finite collection of tori. Topological crossing intersections of stable and unstable manifolds of tori can be found as non-trivial zeroes of certain… (More)

- Joseph Kang, Christina Czart Ciecierski, +5 authors Brian L Hitsman
- Preventive medicine
- 2014

OBJECTIVE
The purpose of this study is to understand how cancer risk behaviors cluster in U.S. college students and vary by race and ethnicity.
METHODS
Using the fall 2010 wave of the National College Health Assessment (NCHA), we conducted a latent class analysis (LCA) to evaluate the clustering of cancer risk behaviors/conditions: tobacco use, physical… (More)

We present (informally) some geometric structures that imply instability in Hamiltonian systems. We also present some finite calculations which can establish the presence of these structures in a given near integrable systems or in systems for which good numerical information is available. We also discuss some quantitative features of the diffusion… (More)

- Marian Gidea, Josep J. Masdemont
- I. J. Bifurcation and Chaos
- 2007

Abstract. The stable and unstable invariant manifolds associated with Lyapunov orbits about the libration point L1 between the primaries in the planar circular restricted three-body problem with equal masses are considered. The behavior of the intersections of these invariant manifolds for values of the energy between the one of L1 and that of the other… (More)

We consider a dynamical system whose phase space contains a two-dimensional normally hyperbolic invariant manifold diffeomorphic to an annulus. We assume that the dynamics restricted to the annulus is given by an area preserving monotone twist map. We assume that in the annulus there exist finite sequences of primary invariant Lipschitz tori of dimension 1,… (More)