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Quasi-Periodic Parametric Perturbations of Two-Dimensional Hamiltonian Systems with Nonmonotonic Rotation Regul. Chaot. Dyn. (IF 1.4) Pub Date : 2024-03-11 Kirill E. Morozov, Albert D. Morozov
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Chaos in Coupled Heteroclinic Cycles Between Weak Chimeras Regul. Chaot. Dyn. (IF 1.4) Pub Date : 2024-03-11 Artyom E. Emelin, Evgeny A. Grines, Tatiana A. Levanova
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On the Regularity of Invariant Foliations Regul. Chaot. Dyn. (IF 1.4) Pub Date : 2024-03-11 Dmitry Turaev
We show that the stable invariant foliation of codimension 1 near a zero-dimensional hyperbolic set of a \(C^{\beta}\) map with \(\beta>1\) is \(C^{1+\varepsilon}\) with some \(\varepsilon>0\). The result is applied to the restriction of higher regularity maps to normally hyperbolic manifolds. An application to the theory of the Newhouse phenomenon is discussed.
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Asymptotics of Self-Oscillations in Chains of Systems of Nonlinear Equations Regul. Chaot. Dyn. (IF 1.4) Pub Date : 2024-03-11 Sergey A. Kashchenko
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On Homeomorphisms of Three-Dimensional Manifolds with Pseudo-Anosov Attractors and Repellers Regul. Chaot. Dyn. (IF 1.4) Pub Date : 2024-03-11 Vyacheslav Z. Grines, Olga V. Pochinka, Ekaterina E. Chilina
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Quasi-Periodicity at Transition from Spiking to Bursting in the Pernarowski Model of Pancreatic Beta Cells Regul. Chaot. Dyn. (IF 1.4) Pub Date : 2024-03-11 Haniyeh Fallah, Andrey L. Shilnikov
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On Bifurcations of Symmetric Elliptic Orbits Regul. Chaot. Dyn. (IF 1.4) Pub Date : 2024-03-11 Marina S. Gonchenko
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Classification of Axiom A Diffeomorphisms with Orientable Codimension One Expanding Attractors and Contracting Repellers Regul. Chaot. Dyn. (IF 1.4) Pub Date : 2024-03-11 Vyacheslav Z. Grines, Vladislav S. Medvedev, Evgeny V. Zhuzhoma
Let \(\mathbb{G}_{k}^{cod1}(M^{n})\), \(k\geqslant 1\), be the set of axiom A diffeomorphisms such that the nonwandering set of any \(f\in\mathbb{G}_{k}^{cod1}(M^{n})\) consists of \(k\) orientable connected codimension one expanding attractors and contracting repellers where \(M^{n}\) is a closed orientable \(n\)-manifold, \(n\geqslant 3\). We classify the diffeomorphisms from \(\mathbb{G}_{k}^{cod1}(M^{n})\)
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Sensitivity and Chaoticity of Some Classes of Semigroup Actions Regul. Chaot. Dyn. (IF 1.4) Pub Date : 2024-03-11 Nina I. Zhukova
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Twin Heteroclinic Connections of Reversible Systems Regul. Chaot. Dyn. (IF 1.4) Pub Date : 2024-03-11 Nikolay E. Kulagin, Lev M. Lerman, Konstantin N. Trifonov
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Numerical Study of Discrete Lorenz-Like Attractors Regul. Chaot. Dyn. (IF 1.4) Pub Date : 2024-01-01
Abstract We consider a homotopic to the identity family of maps, obtained as a discretization of the Lorenz system, such that the dynamics of the last is recovered as a limit dynamics when the discretization parameter tends to zero. We investigate the structure of the discrete Lorenz-like attractors that the map shows for different values of parameters. In particular, we check the pseudohyperbolicity
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Universal Transient Dynamics in Oscillatory Network Models of Epileptic Seizures Regul. Chaot. Dyn. (IF 1.4) Pub Date : 2024-01-01
Abstract Discharges of different epilepsies are characterized by different signal shape and duration. The authors adhere to the hypothesis that spike-wave discharges are long transient processes rather than attractors. This helps to explain some experimentally observed properties of discharges, including the absence of a special termination mechanism and quasi-regularity. Analytical approaches mostly
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Dynamics of a Pendulum in a Rarefied Flow Regul. Chaot. Dyn. (IF 1.4) Pub Date : 2024-01-01
Abstract We consider the dynamics of a rod on the plane in a flow of non-interacting point particles moving at a fixed speed. When colliding with the rod, the particles are reflected elastically and then leave the plane of motion of the rod and do not interact with it. A thin unbending weightless “knitting needle” is fastened to the massive rod. The needle is attached to an anchor point and can rotate
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Slow-Fast Systems with an Equilibrium Near the Folded Slow Manifold Regul. Chaot. Dyn. (IF 1.4) Pub Date : 2023-12-19 Natalia G. Gelfreikh, Alexey V. Ivanov
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Hyperbolic Attractors Which are Anosov Tori Regul. Chaot. Dyn. (IF 1.4) Pub Date : 2023-12-19 Marina K. Barinova, Vyacheslav Z. Grines, Olga V. Pochinka, Evgeny V. Zhuzhoma
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Chaos and Hyperchaos in Two Coupled Identical Hindmarsh – Rose Systems Regul. Chaot. Dyn. (IF 1.4) Pub Date : 2023-12-19
Abstract The dynamics of two coupled neuron models, the Hindmarsh – Rose systems, are studied. Their interaction is simulated via a chemical coupling that is implemented with a sigmoid function. It is shown that the model may exhibit complex behavior: quasi-periodic, chaotic and hyperchaotic oscillations. A phenomenological scenario for the formation of hyperchaos associated with the appearance of
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Circular Fleitas Scheme for Gradient-Like Flows on the Surface Regul. Chaot. Dyn. (IF 1.4) Pub Date : 2023-12-07 Vladislav D. Galkin, Elena V. Nozdrinova, Olga V. Pochinka
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On the Method of Introduction of Local Variables in a Neighborhood of Periodic Solution of a Hamiltonian System with Two Degrees of Freedom Regul. Chaot. Dyn. (IF 1.4) Pub Date : 2023-12-07 Boris S. Bardin
A general method is presented for constructing a nonlinear canonical transformation, which makes it possible to introduce local variables in a neighborhood of periodic motions of an autonomous Hamiltonian system with two degrees of freedom. This method can be used for investigating the behavior of the Hamiltonian system in the vicinity of its periodic trajectories. In particular, it can be applied
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Unifying the Hyperbolic and Spherical $$2$$ -Body Problem with Biquaternions Regul. Chaot. Dyn. (IF 1.4) Pub Date : 2023-12-07 Philip Arathoon
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Stabilization of Steady Rotations of a Spherical Robot on a Vibrating Base Using Feedback Regul. Chaot. Dyn. (IF 1.4) Pub Date : 2023-12-07 Alexander A. Kilin, Tatiana B. Ivanova, Elena N. Pivovarova
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Non-Integrable Sub-Riemannian Geodesic Flow on $$J^{2}(\mathbb{R}^{2},\mathbb{R})$$ Regul. Chaot. Dyn. (IF 1.4) Pub Date : 2023-12-07 Alejandro Bravo-Doddoli
The space of \(2\)-jets of a real function of two real variables, denoted by \(J^{2}(\mathbb{R}^{2},\mathbb{R})\), admits the structure of a metabelian Carnot group, so \(J^{2}(\mathbb{R}^{2},\mathbb{R})\) has a normal abelian sub-group \(\mathbb{A}\). As any sub-Riemannian manifold, \(J^{2}(\mathbb{R}^{2},\mathbb{R})\) has an associated Hamiltonian geodesic flow. The Hamiltonian action of \(\mathbb{A}\)
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Non-Quasi-Periodic Normal Form Theory Regul. Chaot. Dyn. (IF 1.4) Pub Date : 2023-12-07 Gabriella Pinzari
We review a recent application of the ideas of normal form theory to systems (Hamiltonian ones or general ODEs) where the perturbing term is not periodic in one coordinate variable. The main difference from the standard case consists in the non-uniqueness of the normal form and the total absence of the small divisors problem. The exposition is quite general, so as to allow extensions to the case of
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On Phase at a Resonance in Slow-Fast Hamiltonian Systems Regul. Chaot. Dyn. (IF 1.4) Pub Date : 2023-10-20 Yuyang Gao, Anatoly Neishtadt, Alexey Okunev
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On Families of Bowen – Series-Like Maps for Surface Groups Regul. Chaot. Dyn. (IF 1.4) Pub Date : 2023-10-20 Lluís Alsedà, David Juher, Jérôme Los, Francesc Mañosas
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A Remark on the Onset of Resonance Overlap Regul. Chaot. Dyn. (IF 1.4) Pub Date : 2023-10-20 Jacques Fejoz, Marcel Guardia
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Polynomial Entropy and Polynomial Torsion for Fibered Systems Regul. Chaot. Dyn. (IF 1.4) Pub Date : 2023-10-20 Flavien Grycan-Gérard, Jean-Pierre Marco
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Linear Stability of an Elliptic Relative Equilibrium in the Spatial $$n$$ -Body Problem via Index Theory Regul. Chaot. Dyn. (IF 1.4) Pub Date : 2023-10-20 Xijun Hu, Yuwei Ou, Xiuting Tang
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The Siegel – Bruno Linearization Theorem Regul. Chaot. Dyn. (IF 1.4) Pub Date : 2023-10-20 Patrick Bernard
The purpose of this paper is a pedagogical one. We provide a short and self-contained account of Siegel’s theorem, as improved by Bruno, which states that a holomorphic map of the complex plane can be locally linearized near a fixed point under certain conditions on the multiplier. The main proof is adapted from Bruno’s work.
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Hamiltonian Paradifferential Birkhoff Normal Form for Water Waves Regul. Chaot. Dyn. (IF 1.4) Pub Date : 2023-10-20 Massimiliano Berti, Alberto Maspero, Federico Murgante
We present the almost global in time existence result in [13] of small amplitude space periodic solutions of the 1D gravity-capillary water waves equations with constant vorticity and we describe the ideas of proof. This is based on a novel Hamiltonian paradifferential Birkhoff normal form approach for quasi-linear PDEs.
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Three-Body Relative Equilibria on $$\mathbb{S}^{2}$$ Regul. Chaot. Dyn. (IF 1.4) Pub Date : 2023-10-20 Toshiaki Fujiwara, Ernesto Pérez-Chavela
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Compactification of the Energy Surfaces for $$n$$ Bodies Regul. Chaot. Dyn. (IF 1.4) Pub Date : 2023-10-20 Andreas Knauf, Richard Montgomery
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Distance Estimates for Action-Minimizing Solutions of the $$N$$ -Body Problem Regul. Chaot. Dyn. (IF 1.4) Pub Date : 2023-10-20 Kuo-Chang Chen, Bo-Yu Pan
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Total Collision with Slow Convergence to a Degenerate Central Configuration Regul. Chaot. Dyn. (IF 1.4) Pub Date : 2023-07-31 Richard Moeckel
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Aubry Set on Infinite Cyclic Coverings Regul. Chaot. Dyn. (IF 1.4) Pub Date : 2023-07-31 Albert Fathi, Pierre Pageault
In this paper, we study the projected Aubry set of a lift of a Tonelli Lagrangian \(L\) defined on the tangent bundle of a compact manifold \(M\) to an infinite cyclic covering of \(M\). Most of weak KAM and Aubry – Mather theory can be done in this setting. We give a necessary and sufficient condition for the emptiness of the projected Aubry set of the lifted Lagrangian involving both Mather minimizing
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Complex Arnol’d – Liouville Maps Regul. Chaot. Dyn. (IF 1.4) Pub Date : 2023-07-31 Luca Biasco, Luigi Chierchia
We discuss the holomorphic properties of the complex continuation of the classical Arnol’d – Liouville action-angle variables for real analytic 1 degree-of-freedom Hamiltonian systems depending on external parameters in suitable Generic Standard Form, with particular regard to the behaviour near separatrices. In particular, we show that near separatrices the actions, regarded as functions of the energy
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Brake Orbits Fill the N-body Hill Region Regul. Chaot. Dyn. (IF 1.4) Pub Date : 2023-07-31 Richard Montgomery
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Attractive Invariant Circles à la Chenciner Regul. Chaot. Dyn. (IF 1.4) Pub Date : 2023-07-31 Jessica Elisa Massetti
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Emergence of Strange Attractors from Singularities Regul. Chaot. Dyn. (IF 1.4) Pub Date : 2023-07-31 José Angel Rodríguez
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Integrable Systems on a Sphere, an Ellipsoid and a Hyperboloid Regul. Chaot. Dyn. (IF 1.4) Pub Date : 2023-07-31 Andrey V. Tsiganov
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From $$2N$$ to Infinitely Many Escape Orbits Regul. Chaot. Dyn. (IF 1.4) Pub Date : 2023-07-31 Josep Fontana-McNally, Eva Miranda, Cédric Oms, Daniel Peralta-Salas
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On the Uniqueness of Convex Central Configurations in the Planar $$4$$ -Body Problem Regul. Chaot. Dyn. (IF 1.4) Pub Date : 2023-07-31 Shanzhong Sun, Zhifu Xie, Peng You
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Parametric Resonance of a Charged Pendulum with a Suspension Point Oscillating Between Two Vertical Charged Lines Regul. Chaot. Dyn. (IF 1.4) Pub Date : 2023-06-02 Adecarlos C. Carvalho, Gerson C. Araujo
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A Note on the Weighted Yamabe Flow Regul. Chaot. Dyn. (IF 1.4) Pub Date : 2023-06-02 Theodore Yu. Popelensky
For two dimensional surfaces (smooth) Ricci and Yamabe flows are equivalent. In 2003, Chow and Luo developed the theory of combinatorial Ricci flow for circle packing metrics on closed triangulated surfaces. In 2004, Luo developed a theory of discrete Yamabe flow for closed triangulated surfaces. He investigated the formation of singularities and convergence to a metric of constant curvature. In this
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On Partially Hyperbolic Diffeomorphisms and Regular Denjoy Type Homeomorphisms Regul. Chaot. Dyn. (IF 1.4) Pub Date : 2023-06-02 Vyacheslav Z. Grines, Dmitrii I. Mints
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Numerical and Theoretical Studies on the Rational Standard Map at Moderate-to-Large Values of the Amplitude Parameter Regul. Chaot. Dyn. (IF 1.4) Pub Date : 2023-06-02 Pablo M. Cincotta, Claudia M. Giordano, Carles Simó
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Formal Stability, Stability for Most Initial Conditions and Diffusion in Analytic Systems of Differential Equations Regul. Chaot. Dyn. (IF 1.4) Pub Date : 2023-06-02 Valery V. Kozlov
An example of an analytic system of differential equations in \(\mathbb{R}^{6}\) with an equilibrium formally stable and stable for most initial conditions is presented. By means of a divergent formal transformation this system is reduced to a Hamiltonian system with three degrees of freedom. Almost all its phase space is foliated by three-dimensional invariant tori carrying quasi-periodic trajectories
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Twist Maps of the Annulus: An Abstract Point of View Regul. Chaot. Dyn. (IF 1.4) Pub Date : 2023-04-10 Patrice Le Calvez
We introduce the notion of abstract angle at a couple of points defined by two radial foliations of the closed annulus. We will use for this purpose the digital line topology on the set \({\mathbb{Z}}\) of relative integers, also called the Khalimsky topology. We use this notion to give unified proofs of some classical results on area preserving positive twist maps of the annulus by using the Lifting
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V-Shaped Action Functional with Delay Regul. Chaot. Dyn. (IF 1.4) Pub Date : 2023-04-10 Urs Frauenfelder
In this note we introduce the V-shaped action functional with delay in a symplectization, which is an intermediate action functional between the Rabinowitz action functional and the V-shaped action functional. It lives on the same space as the V-shaped action functional, but its gradient flow equation is a delay equation as in the case of the Rabinowitz action functional. We show that there is a smooth
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On $$SL(2,\mathbb{R})$$ -Cocycles over Irrational Rotations with Secondary Collisions Regul. Chaot. Dyn. (IF 1.4) Pub Date : 2023-04-07 Alexey V. Ivanov
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Using Couplings to Suppress Chaos and Produce a Population Stabilisation Strategy Regul. Chaot. Dyn. (IF 1.4) Pub Date : 2023-04-07 Luís M. Lopes, Clara Grácio, Sara Fernandes, Danièle Fournier-Prunaret
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Stability Analysis of Resonant Rotation of a Gyrostat in an Elliptic Orbit Under Third-and Fourth-Order Resonances Regul. Chaot. Dyn. (IF 1.4) Pub Date : 2023-04-07 Xue Zhong, Jie Zhao, Kaiping Yu, Minqiang Xu
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Spiral-Like Extremals near a Singular Surface in a Rocket Control Problem Regul. Chaot. Dyn. (IF 1.4) Pub Date : 2023-04-07 Mariya I. Ronzhina, Larisa A. Manita
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Smale Regular and Chaotic A-Homeomorphisms and A-Diffeomorphisms Regul. Chaot. Dyn. (IF 1.4) Pub Date : 2023-04-07 Vladislav S. Medvedev, Evgeny V. Zhuzhoma
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Analyzing the Motion of a Washer on a Rod Regul. Chaot. Dyn. (IF 1.4) Pub Date : 2023-04-07 Hiroshi Takano
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Spherical and Planar Ball Bearings — a Study of Integrable Cases Regul. Chaot. Dyn. (IF 1.4) Pub Date : 2023-03-10 Vladimir Dragović, Borislav Gajić, Božidar Jovanović
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Integrable Systems Associated to the Filtrations of Lie Algebras Regul. Chaot. Dyn. (IF 1.4) Pub Date : 2023-03-10 Božidar Jovanović, Tijana Šukilović, Srdjan Vukmirović
In 1983 Bogoyavlenski conjectured that, if the Euler equations on a Lie algebra \(\mathfrak{g}_{0}\) are integrable, then their certain extensions to semisimple lie algebras \(\mathfrak{g}\) related to the filtrations of Lie algebras \(\mathfrak{g}_{0}\subset\mathfrak{g}_{1}\subset\mathfrak{g}_{2}\dots\subset\mathfrak{g}_{n-1}\subset\mathfrak{g}_{n}=\mathfrak{g}\) are integrable as well. In particular
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Billiards Within Ellipsoids in the $$4$$ -Dimensional Pseudo-Euclidean Spaces Regul. Chaot. Dyn. (IF 1.4) Pub Date : 2023-03-10 Vladimir Dragović, Milena Radnović
We study billiard systems within an ellipsoid in the \(4\)-dimensional pseudo-Euclidean spaces. We provide an analysis and description of periodic and weak periodic trajectories in algebro-geometric and functional-polynomial terms.
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Quasiperiodic Version of Gordon’s Theorem Regul. Chaot. Dyn. (IF 1.4) Pub Date : 2023-03-10 Sergey V. Bolotin, Dmitry V. Treschev
We consider Hamiltonian systems possessing families of nonresonant invariant tori whose frequencies are all collinear. Then under certain conditions the frequencies depend on energy only. This is a generalization of the well-known Gordon’s theorem about periodic solutions of Hamiltonian systems. While the proof of Gordon’s theorem uses Hamilton’s principle, our result is based on Percival’s variational
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Roller Racer with Varying Gyrostatic Momentum: Acceleration Criterion and Strange Attractors Regul. Chaot. Dyn. (IF 1.4) Pub Date : 2023-03-10 Ivan A. Bizyaev, Ivan S. Mamaev