3 citations · 3 across the 10 of their papers we have counts for
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When Entropy flows: drifting along the route to Chaos
Eran Igra, Valerii Sopin, Yanghong Yu
Consider a smooth one-parameter family of vector fields defined over some smooth manifold transitions from order into chaos. Inspired by the Second law of Thermodynamics, one is le…
Kneading the Lorenz attractor
Łukasz Cholewa, Eran Igra
A Lorenz map is a piecewise continuous map, modeled after an idealized version of the Lorenz attractor. In this paper we settle the following question - how much…
Using Erdős's methods to study Yorke's problems
Eran Igra, Valerii Sopin
In this paper, we study the possible bifurcations of periodic orbits by analyzing them as graphs. In detail, we construct a collection of graphs which are an idealized versions of…
Period-Doubling Cascades Invariants: Braided Routes To Chaos
Eran Igra, Valerii Sopin
By a classical result of Kathleen Alligood and James Yorke we know that as we isotopically deform a map to a Smale horseshoe map we should often expect the…
Unbounded dynamics for three dimensional vector fields
Eran Igra
Consider a three-dimensional vector field which generates a finite number of fixed points - what can we say on its unbounded dynamics? In this paper we tackle this question, an…
Essential dynamics in chaotic attractors
Eran Igra
We prove that if a smooth vector field of generates a sufficiently complicated heteroclinic knot, the flow also generates infinitely many periodic orbits, which persist u…
Removable dynamics in the Nose-Hoover and Moore-Spiegel Oscillators
Eran Igra
We study the dynamics of the Nose-Hoover and Moore-Spiegel Oscillators, and in particular, their topological dynamics. We prove the dynamics of both these systems can be reduced to…
One Dimensional Dynamics and the Rössler attractor
Eran Igra
The Rössler system is one of the best known chaotic dynamical systems, generating a chaotic attractor which, by the numerical evidence, arises by a period-doubling route to chaos.…
Topological lower bounds for the Rössler System
Eran Igra
The Rössler System is one of the best known chaotic dynamical systems, exhibiting a plethora of complex phenomena - and yet, only a few studies tackled its complexity analytically.…
Knots and Chaos in the Rössler System
Eran Igra
The Rössler System is one of the best known chaotic dynamical systems, exhibiting a plethora of complex phenomena - and yet, only a few studies tackled its complexity analytically.…