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1

Anosov, D. V. Dynamical Systems IX: Dynamical Systems with Hyperbolic Behaviour. Berlin, Heidelberg: Springer Berlin Heidelberg, 1995.

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2

V, Anosov D., ed. Dynamical systems with hyperbolic behavior. Berlin: Springer-Verlag, 1995.

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3

Wiggins, Stephen. Normally Hyperbolic Invariant Manifolds in Dynamical Systems. New York, NY: Springer New York, 1994. http://dx.doi.org/10.1007/978-1-4612-4312-0.

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4

Barreira, Luis. Ergodic Theory, Hyperbolic Dynamics and Dimension Theory. Berlin, Heidelberg: Springer Berlin Heidelberg, 2012.

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5

Avila, Artur. Cocycles over partially hyperbolic maps. Paris: Société mathématique de France, 2013.

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6

Barreira, Luis. Dynamical Systems: An Introduction. London: Springer London, 2013.

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7

A, Rand D., and Ferreira Flávio, eds. Fine structures of hyperbolic diffeomorphisms. Berlin: Springer, 2009.

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8

Gaito, Stephen Thomas. Shadowing of weakly pseudo-hyperbolic pseudo-orbits in discrete dynamical systems. [s.l.]: typescript, 1992.

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9

W, Bates Peter. Existence and persistence of invariant manifolds for semiflows in Banach space. Providence, R.I: American Mathematical Society, 1998.

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10

Waddington, Simon. Prime orbit theorems for closed orbits and knots in hyperbolic dynamical systems. [s.l.]: typescript, 1992.

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11

Júnior, Jacob Palis. Hyperbolicity and sensitive chaotic dynamicas at homoclinic bifurcaitons. Cambridge: Cambridge University Press, 1993.

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12

Lani-Wayda, Bernhard. Hyperbolic sets, shadowing and persistence for noninvertible mappings in Banach spaces. Harlow: Longman, 1995.

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13

Kloeden, Peter E. Nonautonomous dynamical systems. Providence, R.I: American Mathematical Society, 2011.

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14

Lani-Wayda, Bernhard. Hyperbolic sets, shadowing, and persistence for noninvertible mappings in Banach spaces. Harlow, Essex, England: Longman, 1995.

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15

Lani-Wayda, Bernhard. Hyperbolic sets, shadowing, and persistence for noninvertible mappings in Banach spaces. Harlow, Essex, England: Longman, 1995.

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16

Coornaert, M. Symbolic dynamcis [i.e. dynamics] and hyperbolic groups. Berlin: Springer-Verlag, 1993.

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17

Margulis, Grigoriy A. On Some Aspects of the Theory of Anosov Systems: With a Survey by Richard Sharp: Periodic Orbits of Hyperbolic Flows. Berlin, Heidelberg: Springer Berlin Heidelberg, 2004.

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18

Li, Daqian. Boundary value problems for quasilinear hyperbolic systems. Durham, NC, U.S.A: Mathematics Dept., Duke University, 1985.

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19

Godlewski, Edwige. Numerical approximation of hyperbolic systems of conservation laws. New York: Springer, 1996.

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20

Center, Ames Research, ed. On the implementation of a class of upwind schemes for system of hyperbolic conservation laws. Moffett Field, Calif: National Aeronautics and Space Administration, Ames Research Center, 1985.

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21

F, Thompson Joe, and United States. National Aeronautics and Space Administration., eds. Semi-annual status report for the period November 15, 1985 through May 14, 1986 ... entitled Transformation of two and three-dimensional regions by elliptic systems. Mississippi State, MS: Mississippi State University, Dept. of Aerospace Engineering, 1986.

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22

F, Thompson Joe, and United States. National Aeronautics and Space Administration, eds. Semi-annual status report for the period November 15, 1985 through May 14, 1986 ... entitled Transformation of two and three-dimensional regions by elliptic systems. Mississippi State, MS: Mississippi State University, Dept. of Aerospace Engineering, 1986.

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23

D.V. Anosov (Contributor, Editor), S. K. Aranson (Contributor), V. Z. Grines (Contributor), R. V. Plykin (Contributor), A. V. Safonov (Contributor), E. A. Sataev (Contributor), S. V. Shlyachkov (Contributor), et al., eds. Dynamical Systems IX: Dynamical Systems with Hyperbolic Behaviour (Encyclopaedia of Mathematical Sciences). Springer, 1995.

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24

Wiggins, Stephen, G. Haller, and I. Mezic. Normally Hyperbolic Invariant Manifolds in Dynamical Systems. Springer London, Limited, 2013.

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25

Wiggins, Stephen, G. Haller, and I. Mezic. Normally Hyperbolic Invariant Manifolds in Dynamical Systems. Springer, 2013.

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26

Wiggins, Stephen. Normally Hyperbolic Invariant Manifolds in Dynamical Systems. Springer, 2013.

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27

Normally hyperbolic invariant manifolds in dynamical systems. New York: Springer-Verlag, 1994.

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28

Anosov, D. V. Dynamical Systems IX: Dynamical Systems With Hyperbolic Behaviour (Encyclopaedia of Mathematical Sciences). Springer, 1995.

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29

Barreira, Luis, and Claudia Valls. Dynamical Systems: An Introduction. Springer, 2012.

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30

Hyperbolic dynamics, fluctuations, and large deviations. Providence, Rhode Island: American Mathematical Society, 2015.

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31

Eldering, Jaap. Atlantis Series in Dynamical Systems: Normally Hyperbolic Invariant Manifolds. We Publish Books, 2013.

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32

Barreira, Luis. Dimension and Recurrence in Hyperbolic Dynamics (Progress in Mathematics Book 272). Birkhäuser, 2008.

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33

(Editor), Giovanni Forni, Mikhail Lyubich (Editor), Charles Pugh (Editor), and Michael Shub (Editor), eds. Partially Hyperbolic Dynamics, Laminations, and Teichmuller Flow (Fields Institute Communications). American Mathematical Society, 2007.

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34

Hyperbolicity Lectures Given At The Centro Internazionale Matematico Estivo Cime Held In Cortona Arezzo Italy June 24july 2 1976. Springer, 2012.

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35

Ergodic Theory Hyperbolic Dynamics And Dimension Theory. Springer, 2012.

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36

Differentiable dynamical systems : an introduction to structural stability and hyperbolicity. AMS, 2016.

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37

An Introduction to Dynamical Systems: Continuous and Discrete (Pure and Applied Undergraduate Texts). American Mathematical Society, 2012.

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38

Tartar, Luc. From Hyperbolic Systems to Kinetic Theory: A Personalized Quest (Lecture Notes of the Unione Matematica Italiana Book 6). Springer, 2008.

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39

Kaloshin, Vadim, and Ke Zhang. Arnold Diffusion for Smooth Systems of Two and a Half Degrees of Freedom. Princeton University Press, 2020. http://dx.doi.org/10.23943/princeton/9780691202525.001.0001.

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Abstract:
Arnold diffusion, which concerns the appearance of chaos in classical mechanics, is one of the most important problems in the fields of dynamical systems and mathematical physics. Since it was discovered by Vladimir Arnold in 1963, it has attracted the efforts of some of the most prominent researchers in mathematics. The question is whether a typical perturbation of a particular system will result in chaotic or unstable dynamical phenomena. This book provides the first complete proof of Arnold diffusion, demonstrating that that there is topological instability for typical perturbations of five-dimensional integrable systems (two and a half degrees of freedom). This proof realizes a plan John Mather announced in 2003 but was unable to complete before his death. The book follows Mather's strategy but emphasizes a more Hamiltonian approach, tying together normal forms theory, hyperbolic theory, Mather theory, and weak KAM theory. Offering a complete, clean, and modern explanation of the steps involved in the proof, and a clear account of background material, the book is designed to be accessible to students as well as researchers. The result is a critical contribution to mathematical physics and dynamical systems, especially Hamiltonian systems.
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40

Analytic and Probabilistic Approaches to Dynamics in Negative Curvature. Springer, 2014.

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41

Dal'Bo, Françoise, Marc Peigné, and Andrea Sambusetti. Analytic and Probabilistic Approaches to Dynamics in Negative Curvature. Springer, 2016.

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42

Geometry and Dynamics in Gromov Hyperbolic Metric Spaces: With an Emphasis on Non-Proper Settings. American Mathematical Society, 2017.

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43

Nekrashevych, Volodymyr. Groups and Topological Dynamics. American Mathematical Society, 2022.

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44

Groups and Topological Dynamics. American Mathematical Society, 2022.

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45

Tartar, Luc. From Hyperbolic Systems to Kinetic Theory. Springer, 2008.

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46

Raviart, Pierre-Arnaud, and Edwige Godlewski. Numerical Approximation of Hyperbolic Systems of Conservation Laws. Springer, 2014.

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47

Raviart, Pierre-Arnaud, and Edwige Godlewski. Numerical Approximation of Hyperbolic Systems of Conservation Laws. Springer New York, 2021.

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48

Raviart, Pierre-Arnaud, and Edwige Godlewski. Numerical Approximation of Hyperbolic Systems of Conservation Laws. Springer London, Limited, 2013.

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49

Nonlinear conservation laws, fluid systems and related topics. Beijing, China: Higher Education Press, 2009.

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50

Liu, Tai-Ping. Shock Waves. American Mathematical Society, 2021.

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